Anthony Martial gave United the lead in the first half from close range against a below-par Wolves.
Nuno Espirito Santo's team markedly improved after the break and Neves found the net with a gorgeous 20-yard curler which beat David De Gea via the crossbar.
United had an opportunity to re-take the lead via a Paul Pogba penalty, but Patricio made an excellent save to earn a point.
So, lightning doesn't strike three times.
It would have been a bit greedy to expect yet another spine-tingling 2-1 win over Manchester United, writes Tim Spiers at Molineux.
But Wolves very nearly did just that. After a deflating first half in which they were most un-Wolves-like in almost everything they did, Nuno Espirito Santo's team galvanised themselves for a rambunctious second half display in which they pegged United back and were the better team, showing the tenacity and the rapscallion nature we've grown so accustomed to in the past two years.
It was largely inspired by Adama Traore, whose pace and bullish attitude frightened the visitors, who had been made to look so comfortable in the first 45 minutes by a worryingly placed Wolves.
Traore, on for the ill Matt Doherty, display exactly the characteristics required in an up-and-at-them display which used his explosive pace, yes, but also showed a maturity in terms of his defensive duties and his end product.
Wolves were indebted to Rui Patricio for an excellent penalty save from Paul Pogba, but they'd more than earned their point, which came via the magical wand that is Ruben Neves' right boot.
When you see Neves grinning as he runs towards the South Bank pointing to his own forehead, you know that art has just been created, and Neves' fifth Premier League goal (he's had three touches in the opposition box in that time) was his best yet, an unsaveable, pinpoint, inch-perfect curler into the net via the bar. It was poetry.
All the signs are that Wolves are ready to repeat what they did last season. They also wouldn't mind playing Manchester United more often – that's four games unbeaten against the Red Devils.
As expected Nuno, who had made nine changes for the 4-0 Europa League win over Pyunik on Thursday, reverted back to the same XI and substitutes from the 0-0 draw against Leicester on the opening weekend.
Manchester United made just the one change, with Daniel James in for his first start for the club.
Wolves will have been hoping for lightning to strike three times after their fabulous 2-1 wins over United last season, but in the first half the opposite was true as the visitors took charge against a flaccid Wolves.
Indeed, Ole Gunnar Solskjaer's team were a different proposition, despite only having three new faces in their side in James, Aaron Wan-Bissaka and Harry Maguire.
Wolves, as they had in the FA Cup win here in March, sat deep early on and looked to soak up pressure. That worked well in the opening stages but the problem was when they tried to transition to the opposition third. Apart from a barnstorming Raul Jimenez run when he dashed from halfway, taking on three players and leaving Maguire on his backside to win a corner, Wolves offered absolutely no attacking threat of note for the entire half.
They were guilty of conceding possession time and again, with Ruben Neves way below his best and Matt Doherty looking off-colour, amid suggestions he was feeling ill.
United on the other hand pressed Wolves expertly to crowd them for room. Wolves failed to do the opposite and the visitors soon took charge.
Shortly after Anthony Martial narrowly failed to get on the end of Marcus Rashford's teasing cross, the combination worked a treat when the Red Devils took the lead.
It was a well-worked strike, with Rashford finding Martial's dart into the box perfectly as he got half a yard on Willy Boly and in-behind Conor Coady before finishing emphatically with a powerful left-footed shot past a helpless Rui Patricio.
The rest of the half was a non-event, save for right on the stroke of half-time when flat Wolves were fortunate not to conceded a second. Bennett played a pass way short of Boly – Martial nipped in but he couldn't get a shot away, to the relief of a frustrated home crowd.
When the whistle blew it was as quiet as Molineux has been for a long time when the players headed for the tunnel, reflective of an underwhelming first 45 minutes in which Wolves made United's life pretty easy.
Adama Traore replaced Doherty at half-time and Wolves immediately improved in terms of their approach and attitude. They got straight on the front foot, with Jonny Castro Otto crossing menacingly into the box where Maguire had to bundle behind ahead of Jimenez.
Traore's pace and intent had helped transform Wolves – and with the momentum with them they soon equalised.
Moutinho worked a short corner, took Jota's pass and then played perfectly to Neves who, from the edge of the box, created yet another work of art with a delicious, mouth-watering curling shot which majestically bounced in off the underside of the bar.
Molineux went potty – but their celebrations were momentarily cut short as the VAR officials checked if Moutinho was offside when he took Jota's pass. It was an extremely tight call but it went Wolves' way, generating loud anti-VAR chants both before and after the decision was made.
Wolves were looking like their normal selves again and, with the raucous crowd playing their part, it was set up for another famous Molineux night against United.
Then, from nowhere, the visitors sliced Wolves open with Pogba gallivanting into the box and going over Coady's statuesque frame, although the skipper's boot did catch the Frenchman.
Pogba stepped up to take the penalty himself – but Rui Patricio produced an excellent save from what was a powerfully-hit effort to keep it out, following up from his three penalty saves in the Asia Trophy shoot-out against Manchester City last month.
United were doing most of the pressing as we approached the 80-minute mark but Wolves, especially via Traore, always carried a threat. The all-action Spaniard had the beating of Luke Shaw – who after being given the runaround previously by Jota here was now being sent for a £2,99 breakfast at Asda – and teed up Otto for a header from 10 yards which De Gea held.
Jimenez then broke at pace, playing to the overlapping Jota whose cross was fired over by Dendoncker as Wolves pushed for a late winner, but to no avail.
19 Chance! United should be ahead after some stunning work from Rashford, whose fancy footwork leaves Bennett on his backside. He then crosses the ball towards Martial, who can't get a touch on it from close range.
27 - Goal! Martial finds the net in emphatic fashion. Rashford's well-weighted pass releases the Frenchman in behind Coady, and he comes up with a powerful first-time finish with his left foot, leaving Patricio helpless.
55 - GOOOOALLLLLL!! What an incredible strike from Neves to bring Wolves level! Picked out on the edge of the box by Moutinho, he takes a touch to set himself before launching a beautiful curler in off the crossbar. Finishing of the highest order.
68 - Penalty SAVED! United win a spot-kick as Pogba is brought down in the box by Coady. Pogba then takes it but sees his powerful effort swatted away by Patricio. Strong work from the Wolves shot-stopper.
Wolves (3-5-2): Patricio; Bennett, Coady (c), Boly; Doherty (Traore, 46), Neves, Dendoncker, Moutinho, Otto; Jimenez (Cutrone, 90), Jota (Neto, 86)
Subs not used: Ruddy (gk), Saiss, Vinagre, Gibbs-White
Goals: Neves (55)
Man United (4-3-3): De Gea; Wan-Bissaka, Lindelof, Maguire, Shaw; McTominay, Pogba; James (Greenwood, 89), Lingard (Mata, 82), Rashford (Pereira, 89); Martial
Subs not used: Romero (gk), Tuanzebe, Young, Matic
Goals: Martial (27)
Attendance: 31,314 (3,014 Man United fans)
Referee: Jonathan Moss
Wolves travel to Turin to face Torino in the first leg of their Europa League play-off on Thursday (8pm) before hosting Burnley in the Premier League on Sunday (4.30pm).