The Railwaymen started the day at the foot of the League One table, following defeats by Brighton and Carlisle United in their opening two fixtures and named recent signing Clayton Donaldson on the bench.
In contrast, the Saddlers had taken four points out of six from their opening two games, with Jabo Ibehre having found the net against both Yeovil Town and Scunthorpe United.
Marco Reich drove an early chance wide of target for the visitors, before Anthony Elding started to cause problems for the Saddlers backline.
He got his reward with 21 minutes on the clock, netting from close range after good work by another summer signing, Joel Grant.
On the half-hour mark, Crewe were indebted to goalkeeper Steve Collis for preserving their lead, as he made an excellent finger-tip save from Reich's close-range header.
Collis then tipped an Alex Nicholls effort over the crossbar as half-time approached, as the visitors began to dictate play.
However, Grant then gave the home side a two-goal cushion right on the interval, ending a superb solo run with a tidy finish past former Alex keeper Clayton Ince.
The Alex started the second period strongly, with Byron Moore twice going close to making it a three-goal lead.
However, on the hour mark the Saddlers were back in the game as experienced midfielder Stephen Hughes rifled in a shot from the edge of the area after Ibehre had touched on a Paul Boertien cross.
That goal put the home side on the back foot and the game became bitty and niggly, with referee Mr Wright issuing four yellow cards in just over ten minutes as play became condensed in midfield.
Walsall continued to press for an equaliser as time ran out, but Crewe held on for their first points of the campaign.