The former Stoke City striker headed in at the far post with six minutes left after substitute Leon Constantine had burst clear down the left wing.
Earlier Martin Allen's battlers forced themselves back on level terms through a John Finnigan penalty as nerves got the better of Gudjon Thordarson's Crewe side on a potentially decisive afternoon.
Victories for rivals Northampton and Brighton have tossed the Icelander's side back into the mix at the wrong end of the table.
But after being given the fillip of a second minute goal from Icelandic Under-21 international Gylfi Sigurdsson, Crewe really should have gone on to win the game comfortably.
Sigurdsson pounced after the Cheltenham defence made a mess of clearing Clayton Donaldson's cross.
The youngster dispatched an impressive volley into the top corner past keeper Scott Brown, who later went on to perform heroics in Cheltenham's rearguard action.
Crewe's decision making around the box was appalling, although they were on top for most of the first half.
John Brayford wafted a few efforts high and wide and Brown tipped Danny Woodards' piledriver over the bar.
Donaldson, after edging past Drissa Diallo, sent his tame effort into Brown's arms.
Cheltenham came out invigorated at the start of the second half with loanees Frankie Artus and David Hutton particularly prominent.
When Hutton dashed down the left side of the box he was upended by a clumsy challenge from Marlon Broomes.
Finnigan, who had only been on the pitch for three minutes, dispatched the resulting penalty down the middle of the goal for his side's 57th minute equaliser.
Sigurdsson whistled a low free-kick inches past the post and Billy Jones forced Brown into a near post save as Crewe tried to get back on top.
Julien Baudet had a 78th minute effort chalked out for offside and Crewe were camped in the visiting half.
They were caught square when substitute Constantine burst through on the left and his cross was deflected into the path of Connor, who grabbed Cheltenham a lifeline or at least postponed their relegation for another week.