The Portuguese frontman opened the scoring for Graham Westley's side, who were coasting with a three-goal lead by the 20th minute after Luke Freeman and Morais again made the most of dismal home defending.
Crewe failed to capitalise on their recent improvement, which had seen them string together back-to-back wins as they offered little quality at either end of the pitch.
Morais ran onto Francois Zoko's flick-on and clipped a classy finish over Steve Phillips in the 10th minute.
Then Freeman doubled the advantage three minutes later, driving in from a tight angle after his initial effort was parried by Phillips.
Morais' second was a classy right-footed chip into the top corner after Crewe centre-half Mark Ellis' tame clearing header landed at his feet.
Greg Tansey drove over with the goal gaping and the visitors continued their assault on the home goal when Zoko clipped an effort onto the near post soon after the interval.
Michael Doughty and substitute James Dunne were also denied by Phillips.
Crewe rarely threatened, although Chuks Aneke should have done better when well placed in front of goal only to poke his shot straight at Chris Day.