The Saddlers have lost just once in 14 games and have gone from bottom of League One two months ago to within four points off the play-offs.
They created the better chances at the Alexandra Stadium, although Elliott Bennett hit the post for the Railwaymen just before half-time.
Evergreen striker Tommy Mooney was always a thorn in the Cheshire side's flesh and he turned and thrashed an early effort into the side-netting from a corner.
Crewe were forced to defend a string of corners all afternoon and it was from one in the second half that Mooney saw his goalbound header cleared off the line by Gary Roberts.
Alex keeper Ben Williams kept his side in it with some super saves.
He turned Daniel Fox's 30-yard special from a tapped free-kick around the post and held onto an angled drive from on-loan Peter Sweeney.
Crewe took until ten minutes before the break to muster a threat when Wolves youngster Bennett saw his shot cannon back off the woodwork.
That was the cue for them to step up their efforts and Nicky Maynard lofted an effort over the top and debutant Mark Carrington shot across the face of goal.
Walsall keeper Clayton Ince had little to do apart from deal with crosses until Alex captain Neil Cox unleashed a 35-yarder which the Trinidadian beat away.
But Michael Ricketts should have won the game for the visitors when a deep corner presented him with an easy header at the far post, but he glanced wide from five yards out.
Crewe technical director Dario Gradi said: "It was a welcome point in many ways.
"Walsall are the form team in League One at the moment and they were playing with a lot of confidence."
Walsall boss Richard Money said: "We did everything apart from score. I don't think many teams will come here and outplay Crewe."