The veteran striker, who signed for the Railwaymen on a short-term deal a week ago, almost provided the decisive touch in a goalmouth scramble to mark his debut.
Byron Moore gave Alex an early lead when he drove into the far corner after Ajay Leitch-Smith slipped a ball inside after 10 minutes.
But Luke Summerfield headed Shrewsbury level when he was left unmarked to direct Marvin Morgan's 28th-minute delivery into the bottom corner.
Alex left-back Gregor Robertson planted a far-post header over after greeting a Kelvin Mellor cross.
But Shrewsbury relied on the excellence of Chris Weale, who made a string of excellent saves after the restart.
The former Leicester City goalkeeper pawed a Leitch-Smith cross-cum-shot away from his top corner and then blocked the same striker's left-footed effort. Weale then denied teenager Max Clayton with a near-post save.
But Crewe were nearly caught out by a swift Shrews counter attack that almost produced a fourth goal in five games for Bolton loanee Tom Eaves.
The towering striker was denied by Alex keeper Steve Phillips, who was smartly of his line.
Sub Ellington went close to stealing the win before Shrewsbury had later penalty appeals turned down after Rob Purdie fell in the box.