Kennedy, last on target in the 3-3 draw against Manchester City in April 2004, salvaged a draw for Wolves in first-half stoppage time when he cancelled out a sixth minute opener from 17-year-old Billy Jones.
Crewe were more pleased with the point than Wolves as it ended a run of seven successive defeats for Dario Gradi's side, who are undefeated in their last four visits to Molineux.
They could have even pulled off a famous win with Wolves goalkeeper Stefan Postma denying Steve Jones with a vital save four minutes from time.
The stalemate just extended Wolves' dismal run that has seen them slip out of promotion race and unsurprisingly they were booed off the pitch by their disgruntled fans.
They have now won just three of their last 13 league games and Hoddle's dream of guiding Wolves back into the Premiership has all but disappeared for another season.
Billy Jones stunned Molineux into silence by firing Crewe ahead from close range when he converted a left-wing cross from Steve Jones.
Wolves took the rest of the half to come to terms with the shock of falling behind and Crewe should really have taken advantage to increase their lead.
Lively striker Luke Rodgers crashed a long-range drive against the bar after a mistake by Joleon Lescott in the 26th minute.
Two minutes later Rodgers was denied by Postma when he let fly from 20 yards.
Postma then beat away a 32nd minute free-kick by Billy Jones as Wolves were run ragged.
Fortunately for Wolves they were able to ride their luck and force themselves back on to level terms in first-half stoppage time.
Kennedy cut in from the right wing and drilled in a low left-foot drive that slipped under the outstretched hand of goalkeeper Ross Turnbull.
While Turnbull was powerless to prevent Kennedy's equaliser, he proved to be a thorn in Wolves' side as they went in search of a second-half winner.
He pulled off stunning saves to deny Denes Rosa and Lee Naylor before tipping away a close-range shot from Tomasz Frankowski in the 67th minute.
Crewe were content to try and catch Wolves on the break and it was a tactic that very nearly paid off.
Twice it needed last-ditch challenges from central defender Jody Craddock to bring to an end menacing runs by Steve Jones and Billy Jones before Postma's late heroics.