So it seems that austerity really does pay after all. After seeing Bebe mark his Manchester United debut with a goal, Sir Alex Ferguson sent on Javier Hernandez to rescue his side for the second time in three days.
Both signings were seen as evidence of how United's spending had been squeezed and, while it is still too early to make a real judgement on the Portuguese Bebe (who Ferguson had not even seen play when he signed him for £7.4m this summer), Hernandez is already looking the real deal.
After a dreadful opening period with only a couple of chances, Bebe's cross looped in off George Elokobi 10 minutes into the second half, only for the Wolverhampton defender to equalise just before the hour mark. Park Ji-sung restored United's advantage, but Kevin Foley replied for the visitors, pushing the tie towards extra time.
After he scored two goals in the 2-1 win over Stoke at the weekend, the introduction of Hernandez 10 minutes from time created a buzz around Old Trafford and he justified that in the final minute, picking the ball up on half way and swapping passes with Darron Gibson before firing past Wayne Hennessey to send United into the quarter-finals.
Wes Brown claimed that Hernandez's goals (he has scored five in his last six appearances) have already given him a position of responsibility at Old Trafford, where a crowd of just 46,083 was present last night.
"He's got great attitude and he just wants to learn," Brown said. "He tries his hardest and did it for us in the end. He's a cult hero already and he'll keep it going."
Hernandez – known by many as Chicharito but as "Jonny on the spot" by Wolves manager Mick McCarthy – cost just £7m in the summer and is key to the positive future Ferguson sees ahead for United.
"We tend to build up heroes very quickly here but the boy is justifying the praise," Ferguson said. "He's got such great potential, the kid. He's the first out on the training ground every day and he's getting a lot of credit and praise – quite rightly.
"You just know when he came on that if he gets a chance, he'll take it. His touch is improving, his control of the ball, his vision is improving and we care about our training and make sure the players do improve.
"It's a bright future. We work hard at producing young players and that's the foundation of the next team."
Ferguson's words were certainly borne out by his choices for United's starting line-up, with young goalkeeper Ben Amos making his first start in two years, Fabio impressing at left-back and Chris Smalling putting in another steady performance.
The opening period gave little indication of what was to come after the interval. From a free-kick delivered by Stephen Hunt, making his first start for Wolves since joining from Hull in the summer, Christophe Berra climbed higher than Gabriel Obertan and flicked on, only for Sylvan Ebanks-Blake to head wide of goal.
Bebe caused Elokobi plenty of problems and was always willing to take on the Wolves full-back and cross at the earliest opportunity.
Michael Carrick, with just one Premier League start this season, went close with two efforts from distance either side of half-time.
Ten minutes after the interval, Bebe pulled United in front. The ball was knocked wide to the winger, he drove into the area and hit a shot that looped up off Elokobi and crossed the line before Foley could head it away.
As the Portuguese danced in celebration and Rio Ferdinand and Nani grinned up in the directors' box, Ferguson must have felt a familiar surge of vindication.
Elokobi made amends just a couple of minutes later when he thumped in a header from a David Jones corner.
Hunt almost put Wolves ahead when he was picked out by a Matt Jarvis cross and his shot hit the bar, but United were pouring forward and soon regained the lead.
Federico Macheda's run was halted by a Steven Mouyokolo block and Park curled in a shot on the turn from the edge of the area.
Wolves, who have not won in the Premier League since the opening day of the season, kept coming and after Gibson gave up possession in midfield, Ebanks-Blake fed Steven Fletcher, who was held up by Jonny Evans, only for Foley (left) to guide a shot past Amos.
But Hernandez was sent on with one purpose and did his job to keep United on track for a third successive Carling Cup.
"I watched Hernandez at Stoke and, forget his goals, his all-round performance was terrific," McCarthy said. "They threw on 'Jonny on the spot' and he scored the winner. He's a terrific player and he punished us."
Manchester United (4-3-3): Amos; Brown, Evans, Smalling, Fabio (Neville, 74); Park (Morrison, 90) Carrick, Gibson; Macheda, Obertan, Bebe (Hernandez, 81). Substitutes not used Rafael, Kuszczak, Brady, Eikrem.
Wolverhampton Wanderers (4-4-2): Hennessey; Foley, Mouyokolo, Berra, Elokobi; Hunt, Jones, Mancienne, Jarvis (Doyle, 85); Ebanks-Blake (Bent, 80), Fletcher. Substitutes not used Hahnemann, Van Damme, Edwards, Stearman, Milijas.
Referee M Jones (Cheshire).