They took the lead just before half-time when a Joao Moutinho free-kick was diverted past his own goalkeeper by Bremer.
Diogo Jota made it 2-0 after great work from Adama Traore before Torino pulled one back through Lorenzo De Silvestri.
Raul Jimenez then scored a stunning solo goal with 18 minutes to go as Wolves went into a handsome first-leg lead before Andrea Belotti's late penalty gave Torino hope for the return at Molineux next week.
The last time Wolves played in this stadium they produced a famous result on their journey to the UEFA Cup final.
While the final of this season's tournament in Gdansk is an awful long way away, you wouldn't bet against Wolves using another memorable Turin performance as a springboard to do something special in Europe once more, writes Tim Spiers at Stadio Olimpico Grande Torino.
In 1972 it was Jim McCalliog's goal which earned Wolves a draw against Juventus with the likes of Kenny Hibbitt and John Richards in their side. In 2019 the likes of Diogo Jota and Raul Jimenez are going a long way to making themselves every bit as legendary in the hearts of the Wolves supporters who can scarcely believe this is happening to their club.
This was seventh in Serie A versus seventh in the Premier League, but after an even first half it was Wolves who inprinted their style, their swagger and their skill on this tie to put one foot in the Europa League group stages.
There were several stand-out performers including Conor Coady, Willy Boly, Joao Moutinho and the scintillating Adama Traore, while Diogo Jota and Raul Jimenez did the business in front of goal, as they have so often in 2019.
Yet again this showed that Nuno's Wolves simply don't crumble on the big occasion, in the white hot atmosphere of a passionate Italian stadium. They rose to the challenge, they kept their discipline and their shape and then gradually their superior quality shone through.
Questions have been asked as to whether they can combine Premier League and Europa League football. Well, a few weeks in, and having made a few changes here just three days after they were physically and mentally drained after a big effort was required against Manchester United, they're answering in exactly the right manner.
These are heady days indeed – and you feel there's plenty more to come.
Nuno sprang a couple of surprises with his team news, selecting Adama Traore and Ruben Vinagre at wing-back, Romain Saiss and midfield and Real Madrid loanee Jesus Vallejo in defence. Jonny Castro Otto, Ruben Neves and Ryan Bennett dropping to the bench, while there was no place in the squad for Matt Doherty who travelled but has suffered with illness against Manchester United.
Torino, whose league campaign doesn't start until Sunday had, like Wolves, easily brushed aside inferior opposition in their first two Europa League qualifiers and had dangerous Italian internationals Andrea Belotti and Simone Zaza up front.
With seventh from last season's Premier League playing seventh from Serie A, it was no surprise that there was little to choose between the two sides in an engrossing first half.
At the beautiful Stadio Olimpico the home fans created a cacophony of noise at both ends of the ground as the 1,500 Wolves fans tried to make themselves heard.
Nuno's team made a solid start, sitting fairly deep and keeping their passing simple as they looked to quieten the home supporters.
It was Wolves who created the game's first chance when Traore, picking up where he left off against United, went on a barnstorming run down the right and cut the ball back for Diogo Jota, who should have done better with a free shot but put it too close to the keeper.
Traore clearly had the beating of his man Christian Ansaldi. He barged past the Argentine and cross towards Raul Jimenez but a defender cleared just in time.
Talking of clearing just in time, Conor Coady did plenty of that as the centre-half put in a true captain's display in the first half, repelling several Torino attacks.
Alongside him Willy Boly was a man mountain and Vallejo was calm and composed. In front of them Joao Moutinho came into his own with the midfield general running the show.
Torino carried a menacing threat, though, and with their first chance they were within inches of taking the lead, with Belotti's cross headed against the crossbar and over by Nicolas Nkoulou.
Back came Wolves with Leander Dendoncker heading marginally wide from Moutinho's free-kick, before Belotti curled not far wide at the other end and then saw his close-range header from a tight angle blocked by Rui Patricio.
It was an even contest – but Wolves broke the deadlock just before the break and nabbed a crucial away goal in the process.
Moutinho's right boot was yet again Wolves' inspiration – he curled a free kick towards Romain Saiss and the ball came off midfielder Bremer past keeper Salvatore Sirigu for an own goal which sent the travelling fans potty.
The hosts looked to gain the initiative at the start of the second-half but Wolves did a great job of keeping Patricio's involvement to a minimum.
Coady, again, was involved when he got a toe on the ball at the perfect moment with Belotti shaping to shoot, before Zaza fired into the side netting.
Wolves continued to look threatening on the break though and they were in dreamland when Jota doubled their lead.
Traore, for the umpteenth time, beat Ansaldi and then picked his moment to perfectly pick out the unmarked Jota who finished from 10 yards.
That deflated the home fans but two minutes later they were celebrating as Torino pulled one back, via a free Lorenzo De Silvestri header.
With the momentum with Torino, Nuno called for Jonny Castro Otto for some defensive stability in place of Traore.
But Wolves continued to search for goals and they should have had a third when Jota played a gorgeous ball over the top for Jimenez, who instead of shooting early on his right foot cut back onto his left and the shot was blocked.
Just a couple of minutes later Jimenez made up for that in sensational style as Wolves took control of the tie.
The Mexican ran from deep, put one defender on his backside and mesmerised a couple more with his direct run, before oh-so-coolly slotted left-footed past helpless keeper Sirigu, sparking wild celebrations in the disbelieving away end.
Wolves were in charge, but a daft foul by Vinagre on Belotti handed Torino a chance to keep it alive, which they duly did when Belotti slammed the resulting penalty under Patricio in the closing minutes.
Torino (3-5-2): Sirigu; Izzo, N'Koulou, Bremer; De Silvestri, Meite (Rincon, 64), Baselli, Berenguer (Lukic, 59), Ansaldi (Aina, 71); Zaza, Belotti
Subs not used: Rosati, Bonifazi, Millico, Djidji.
Goals: De Silvestri (61), Belotti (pen 89)
Wolves (3-5-2): Patricio; Vallejo, Coady (c), Boly; Traore (Otto, 64), Moutinho, Saiss, Dendoncker, Vinagre; Jimenez (Cutrone, 76), Jota (Neto, 69).
Subs not used: Ruddy, Bennett, Neves, Gibbs-White
Goals: Bremer (OG, 43), Jota (59)
Referee: Artur Dias (Portugal)
Wolves host Burnley in the Premier League on Sunday (4.30pm). The return leg against Torino is next Thursday at Molineux, kick off 7.45pm.