But Bruno Lage’s brave team selection seemed destined for failure after his side flattered to deceive in the first half and failed to seriously test the Saints defence.
They marginally improved in the second half before Jimenez latched onto a long ball from goalkeeper Jose Sa just after the hour mark. The striker danced past two defenders and calmly slotted the ball home in front of the away end.
Wolves had to endure some serious Southampton pressure in the closing stages of the game but they stood firm to pick up their second win of the season, with Jimenez’s goal coming only three days before the 10-month anniversary of his injury.
Lage made three shock changes from the team’s last Premier League outing, but stuck with the 3-4-3 formation.
Ruben Neves, Adama Traore and Francisco Trincao all dropped to the bench as Leander Dendoncker, Hwang Hee-chan and Daniel Podence came in. It was also Hwang’s full league debut.
The trio that were introduced into the side all impressed against Tottenham Hotspur in the Carabao Cup on Wednesday and were rewarded by keeping their place, despite replacing three players who have been key to Wolves’ start to the season.
Willy Boly, however, did not keep his place from the cup exploits and was among the substitutes as Romain Saiss returned to the side.
Yerson Mosquera and Rayan Ait-Nouri both missed out through injury, with the latter adhering to concussion protocols and missing one game. That meant Lage brought in two youngsters with Luke Cundle and goalkeeper Louie Moulden on the bench.
Ralph Hasenhuttl made one change to his Southampton side following their 0-0 draw with Man City, starting in a 4-4-2 formation.
Mohammed Salisu came in at centre-back, replacing Jack Stephens.
Within the first 50 seconds of the game Wolves should have taken the lead. Hwang, who started on the left, drifted inside and slipped the ball through for Nelson Semedo. With only Alex McCarthy to beat, the wing-back directed his shot straight at the goalkeeper.
With the early momentum swinging the way of the visitors, it was almost disrupted when Max Kilman played a poor ball across his defence and handed it straight to Mohamed Elyounoussi. The winger took aim from distance but had his effort blocked by Saiss.
Wolves were breaking into the final third nicely at times but then slowing the play down too much and failing to penetrate the defence with the ball final. Conor Coady was consistently spraying sublime cross-field balls to Semedo in space, but on the left Fernando Marcal and Hwang were struggling to combine after 20 minutes.
Marcal was then extremely lucky that team-mate Dendoncker bailed him out and made a good tackle after the defender lost the ball on the edge of his own box. Wolves were struggling to pass the ball out from goalkeeper Sa, to Lage’s frustration on the touchline.
Too many stray passes and lacklustre attacking phases were also frustrating the travelling supporters, who were calling for their team to up the tempo.
But once again poor positioning from Marcal allowed Valentino Livramento to get down the flank and cross for Che Adams. Only superb last ditch defending from Coady denied him.
Moments later Nathan Redmond had the ball in the net but, fortunately for Wolves, was a yard offside and it was spotted by the officials. Then, Sa almost got caught on the ball as the visitors again tried and failed to pass out from the back.
Southampton were gaining momentum in the final minutes of the first half and had the home crowd behind him, but neither team could find a breakthrough before the break as they entered half-time drawing 0-0.
Wolves’ first half was summed up by the final touch of the ball. They had a free-kick and sent everyone up for it before Joao Moutinho played it short. Referee Andy Madley then instantly blew his whistle to the dismay of the Wolves players. Overall, Marcal struggled in the first half, while Podence gave the ball away too often.
Perhaps surprisingly, Lage made no changes at half-time as his side attempted to right the wrongs of the first 45.
But the first big chance of the half fell to Southampton and youngster Livramento. The ball was worked to the right-back inside the box but his shot was just saved by Sa. Moments later the goalkeeper made a superb double save, first to deny a fierce shot from Elyounoussi on the edge of the box, and then to smother Adams’ follow up.
Wolves then responded with a chance of their own through Jimenez. The striker first tried to turn in the box but was dispossessed, before Moutinho played in him down the right side and his low cross was cut out just ahead of Hwang.
Then, just after the hour mark, Wolves got their goal. It was a prime strike from Jimenez who brought down a long ball from Sa, bullied one Saints defender and then cut inside another before showing extremely impressive composure to direct a low effort beyond McCarthy.
Redmond had a shot held by Sa in the aftermath of the opening goal, before Wolves began to sit deeper in the hope of holding onto their lead.
Saints were almost handed a gift after they cleared a Wolves corner. Semedo, as the last man, attempted to clear it but instead smashed the ball off Armando Broja. Sa raced out and cleared it for Wolves, before the referee gave a handball on Broja anyway. It was certainly a heart in mouth moment for Wolves.
Saiss then saved his side with a last ditch tackle on substitute Shane Long, who poked the ball towards goal from close range. With 10 minutes remaining, the hosts were pushing for an equaliser.
Neves was brought on after 87 minutes, replacing Hwang, as Wolves attempted to pack out the midfield and soak up the Saints pressure in the final moments of the game.
Late into stoppage time Jimenez almost got a second when he found space in the box but with a tight angle his shot was saved.
Wolves rode a Southampton storm for most of the six minutes of added time and were able to see out the result, handing Lage his second Premier League win since taking charge.
Wolves: Sa, Kilman, Coady, Saiss, Semedo (Hoever, 87), Dendoncker, Moutinho, Marcal, Podence (Traore, 70), Hwang (Neves, 87), Jimenez.
Subs not used: Ruddy, Moulden, Boly, Cundle, Traore, Silva.
Southampton: McCarthy, Livramento, Bednarek, Salisu, Walker-Peters (Long, 74), Elyounoussi, Romeu, Ward-Prowse, Redmond (Djenepo, 64), Armstrong, Adams (Broja, 64).
Subs not used: Forster, Perraud, Valery, Lyanco, Diallo, Tella.