Westley, whose tumultuous 13-month spell as North End boss ended when he was sacked in February, saw his side fall behind when Paul Huntington headed in on the stroke of half time.
Scott Laird then grabbed his first goal of the season in the 59th minute and Kevin Davies wrapped up the three points for the hosts when he fired home with six minutes to go.
Preston created the better chances early on and only the frame of the goal denied first Stuart Beavon and then Iain Hume.
At the other end, Bailey Wright did brilliantly to block Roarie Deacon's shot on the line before the Stevenage left-back then fired over from the rebound after 41 minutes.
Huntington headed in Laird's cross in the 45th minute to give Preston a deserved lead.
Former Stevenage man Laird then doubled the advantage by heading in Chris Humphrey's cross just before the hour-mark.
And summer signing Davies rounded off the victory with a low strike after 84 minutes to ensure Preston remain unbeaten in the league so far this season.