Rovers had a chance to get something from the game but, with the score at 2-1 in the second half, Jean-Louis Akpa Akpro shot wide from a great chance created by Ryan Lowe in the 58th minute.
Walsall made a flying start, taking the lead inside the first two minutes when, following a short corner, Adam Chambers whipped a low cross into the box for Westcarr to hammer into the roof of the net.
Tranmere could not cope with the home side's quick raids and, after several close shaves the Saddlers went further ahead, Westcarr finding Milan Lalkovic, on loan from Chelsea, who marked his debut with a low drive inside the far post.
Goalkeeper Owain Fon Williams kept Tranmere in the game with several good saves and the visitors halved the lead five minutes from half-time, skipper Andy Robinson bending a great free-kick from left of the penalty box beyond the reach of Richard O'Donnell.
Rovers improved in the second half but Lalkovic opened up their defence for Westcarr to add the third in the 70th minute.