Stevenage were renowned for their determined style in Westley's previous spell in charge and their high-tempo game proved too much for Crewe, who were undone three times inside 10 first-half minutes at Gresty Road.
Portuguese striker Morais was cool and composed when he ran on to Francois Zoko's flick-on and clipped a classy finish over keeper Steve Phillips in the 10th minute.
Luke Freeman then doubled the advantage three minutes later when he drove in from a tight angle after his initial effort was parried by Phillips.
Morais then produced an outstanding finish for the third as he made the most of Mark Ellis's tame clearing header and lofted right-footed shot into the far corner for his fifth goal of the campaign.
Westley said: "The whole mentality of the team has changed. The winning mentality is coming back to this club. It's been hard to create that, but it's the one we've instilled over the years and we've managed to get it back.
"We saw that here because the lads worked hard for their win.
"We made out intentions clear in the first 10 minutes. And we looked like we always had a goal in us.
"The combination play of Filipe and Francois was too hot for Crewe to handle in the first-half. And the combination play of our front four was really exciting at times.
"We're looking as though we are going to get goals at the moment."