A goal six minutes from time from Nick Montgomery ended ten-man Sheffield United's dismal run of form at Gresty Road.
Neil Warnock's Blades suffered four consecutive defeats to dent their automatic promotion hopes in Division One.
When veteran Mike Whitlow was sent off midway through the first half it appeared the Yorkshire side would have their work cut out holding on for anything against the lively looking Crewe team.
But Warnock, who had rested experienced midfielder Stuart McCall, was able to rely on other sources of inspiration for a battling victory.
Seventeen-year-old striker Jonathan Forte was handed his first start and was a revelation for the visitors with his strong running causing havoc in Crewe's back line.
And former Crewe man Ashley Ward led the line with a bustling presence which the Railwaymen were never able to cope with.
Sheffield also had an in-form Michael Tonge running the show in midfield and he tested home keeper Clayton Ince with an early rasping drive from 20 yards Whitlow who had earlier been booked for a foul on Dean Ashton was caught out in the 27th minute when Ashton's flick released Craig Hignett.
The veteran forward, in the second game of his month's loan from Leicester, was tripped by Whitlow as he bore down on goal and the centre-half was unsurprisingly handed a straight red.
Despite being down to ten men, the Blades continued to press Crewe and when Forte broke away from Anthony Tonkin, Ince's parry only teed up Montgomery, whose rebound effort was scrambled away for a corner.
Forte was playing without any fear, his rising drive just before half-time only cleared the bar by inches.
And shortly after the break, he appeared to have caught Ince out with another blockbuster which the keeper could only push towards his own goal and was grateful that Steve Foster was well positioned to head clear over his own crossbar.
Sheffield rammed home the pressure from successive corners with Ince pushing Andy Parkinson's shot over, Hignett clearing off the line from a Ward header, it was all United.
But Crewe were handed a lifeline when Phil Jagielka tripped Steve Jones in the 68th minute and the referee kindly awarded the hosts a penalty, but Ashton blazed his spot-kick high over the bar and Crewe were made to pay when Warnock's side snatched a deserved winner six minutes from time.
Sub Peter Ndlovu scrambled free on the right of the box and in the melee that followed his cross, Montgomery looped a header over the stranded keeper and a couple of defenders.