A positive first half display on Merseyside was overshadowed by Jimenez’s knee injury that could see him miss Sunday’s huge clash.
Wolves seemed set to force penalties on the night, but eventually conceded as Charly Alcaraz put the hosts through to the fourth round with an 80th minute finish.
Analysis
Cesar Peixoto made nine changes from the side that beat Sheffield United at the weekend, as he keeps one eye on the Black Country derby this weekend.
Jackson Tchatchoua and Ladislav Krejci were the only two players to keep their place, as Joao Virginia and Ghislain Konan made their debuts and Sean Neave got his first start.
Krejci starting was a surprise, as was a start forl Jimenez, considering the importance of Sunday’s match with West Brom.
Unsurprisingly, key players Andre, Fer Lopez, Jose Sa and Rodrigo Gomes were not involved in the squad, as Jean-Ricner Bellegarde and new signing Bertrand Traore made their first squads of the season.
David Moyes named a strong Everton starting line-up, as they eyed a place in the next round.
Despite that, it was Wolves that made a strong start to the game as they played the ball around confidently and found space on both flanks to exploit.
Neave had made a good start on the right flank, but on one occasion as Tommy Doyle released him, he rushed his pass for Tawanda Chirewa and wasted a good counter attacking opportunity.
The Newcastle loanee then did well to dance into the box and go down looking for a penalty, but nothing was given.
But for all the positivity in the performance, Wolves were dealt a blow in the 38th minute when Jimenez was forced off with an apparent knee injury - proving starting the striker was an unnecessary risk.
Everton were pushing for an opening goal late in the first half, as Jack Grealish had an effort palmed away by Virginia.
The hosts should have scored on the stroke of half-time when James Garner’s cross found unmarked Thierno Barry at the back post, but his header was denied by a world class Virginia save.
Wolves had a good chance 10 minutes into the second half when Neave battled for the ball and charged forward, before feeding Adam Armstrong, who had a shot saved.
The Toffees were creating several chances by the hour mark, but the score was still locked at 0-0.
Virginia was called into another save when Brennan Johnson was played in, but the goalkeeper made a block with his feet.
The deadlock was finally broken in the 80th minute when Alcaraz picked the ball up inside the box, turned beyond Toti Gomes and curled the ball into the far corner.
Wolves fought to respond quickly and Doyle had a volley saved, but they were unable to find an equaliser as the club’s Carabao Cup campaign came to an end.
Key Moments
GOAL 80 Alcaraz finds a late winner for the hosts
Teams
Wolves: Virginia, Tchatchoua (Trippier, 73), Toti, Krejci (Djiga, 45), Konan, Traore, James (Bellegarde, 63), Doyle, Chirewa (Traore, 73), Neave, Jimenez (Armstrong, 48).
Subs not used: Ruddy, Bueno, Munetsi, Mane.
Everton: Pickford, Maitland-Niles, O’Brien, Keane, Mykolenko, Hackney (Alcaraz, 77), Garner, Dibling, Dewsbury-Hall, Grealish (George, 77), Barry (Johnson, 58).
Subs not used: Travers, King, Branthwaite, Tarkowski, Olayiwola, Graham.
Poor decision by the manager good performance though.I was impressed with that keeper, could be pushing Sa and I thought there were several strong showings amongst a largely second string
can’t believe he risked Raul .. Now look .. clueless as to what Sunday means to us