In his first game in charge Bruno Lage named a strong team but in the blazing heat they failed to get going.
Young midfielder Taylor Perry was arguably Wolves’ best player in a drab first half showing in which Crewe looked most lively.
After introducing eight academy players at half-time, the youngsters started poorly and quickly fell behind from a Christopher Long tap-in.
The much-changed Wolves side did begin to look after the ball better as the half progressed, but failed to threaten going forward and were condemned to defeat on their first pre-season outing.
Lage named a largely experienced starting XI for his first Wolves game in charge, opting for a 4-4-2 formation.
With several first-team players yet to join the group following the European Championships, and Jonny Castro Otto, Pedro Neto and Daniel Podence injured, Lage did start several of the stars available to him.
Francisco Trincao, who recently signed on-loan from Barcelona, lined up alongside Fabio Silva and Jimenez - who made his return following an eight-month lay-off due to his fractured skull injury.
Youngster Perry also started in midfield just two weeks after signing a new two-year deal.
Wing-back Rayan Ait-Nouri started at left-wing, with Fernando Marcal at left-back.
On an extremely warm afternoon at The Alexandra Stadium the hosts welcomed Jimenez back to a football field with a special message from the stadium announcer - which was applauded by the Crewe fans.
A small number of Wolves supporters had also made their way inside and were making themselves heard as the game got underway.
Lage’s men started the game brightly and were aggressive in attacking areas, with many of the forward-thinking players playing high up the pitch. After five minutes Ait-Nouri turned superbly in midfield and fed Silva. The striker looked for his partner Jimenez in the box but the ball was intercepted.
The hosts did not sit back either, however, and had some opportunities of their own. Most notably, Charlie Kirk arrived at the back post to meet a free-kick but his half-volley flew over the bar.
Perry was impressing in the middle of the park for Wolves with some handy ball distribution and confidence in possession. His midfield partner Morgan Gibbs-White was having less joy, however, with a few slack touches. He was fortunate not to be booked too when he dragged Callum Ainley back as he raced down the wing.
A drinks break for both teams then followed as they battled with the soaring temperatures.
With the game back underway a lack of communication between Marcal and John Ruddy allowed Owen Dale a free header at the back post, but the goalkeeper recovered to make a save.
An effort from Long then flashed wide as Crewe asserted some dominance at the 30th minute mark.
Despite that, Wolves almost took the lead when Jimenez’s deflected free-kick from 25 yards wrongfooted goalkeeper Dave Richards and clipped the crossbar on it’s way over.
After 34 minutes the Mexican striker was then substituted, marking a successful comeback from his injury. Patrick Cutrone replaced him.
The Italian forward should have scored when he was played through on goal and, when on the stretch, he reached the ball before Richards. But the goalkeeper was able to save.
That was the last action of the half as Wolves entered the break drawing 0-0.
Lage made eight changes to his side at half-time, giving many of his youngsters a chance to impress. Only Ruddy, Max Kilman and Cutrone stayed on the field from the first half as they continued with the 4-4-2 formation.
Within minutes Cutrone had a chance to score, too. He was handed the ball on a plate inside the box by Renat Dadashov but his deflected effort blazed over the bar.
After 53 minutes Crewe took the lead. Wolves switched off from a short corner and after Kirk got beyond Hugo Bueno and raced into the box, he crossed for Long who tapped home from two yards. The defending was far too pedestrian from Wolves who reacted slowly.
Despite the poor start to the half Wolves’ youngsters began to see more of the ball after 65 minutes. Kilman, with his last action before coming off for Romain Saiss, produced a delightful cross-field ball for Jack Scott who took the ball down well. He then crossed for Dadashov who had his shot blocked.
Crewe should have doubled their lead when Oli Finney got the better of Owen Otasowie and rounded Ruddy, but after delaying his shot his eventual effort was blocked by Scott.
Eventually Wolves did test Jaaskelainen as the goalkeeper got down well to deny Cutrone.
But in the end they failed to breakthrough and Wolves fell to a 1-0 defeat.
Crewe: Richards (Jaaskellainen, 62), Ramsay, Adebisi (Sass-Davies, 62), Murphy (Griffiths, 62), Hoban (Johnson, 62), Offord (Daniels, 62), Ainley (Lundstram, 62), Finney, Long, Kirk (Robbins, 62), Dale.
Wolves: Ruddy, Hoever (Scott, 45, Lonwijk, 88), Boly (Marques, 45), Kilman (Saiss, 66), Marcal (Bueno, 45), Trincao (Cundle, 45), Gibbs-White (Otasowie, 45), Perry (Estrada, 45), Ait-Nouri (Campbell, 45), Silva (Dadashov, 45), Jimenez (Cutrone, 34, Samuels, 88)
Subs not used: Moulden, Sondergaard.