Rovers' reply came courtesy of a Curtis Obeng own goal with two minutes left but by then the damage had been done as Charles and Mousinho added to Jimmy Smith's first-half strike as the home side stretched their unbeaten run to four league games.
After a quiet opening period Smith struck after 21 minutes when he charged down a clearance and calmly stroked the ball home.
Stevenage should have grabbed a second goal before half-time but both Luke Freeman and Bira Dembele were denied by smart saves from Owain Fon Williams, while Lucas Akins also prodded wide when through on goal.
But the hosts did double their lead midway through the second half after Akins cut the ball back for Charles to fire home.
And just three minutes later Mousinho made the game safe with a wonderful curling effort that went in off the post with 74 minutes on the clock.
Tranmere did grab a consolation when Obeng put the ball into his own net following a mix up with his goalkeeper Chris Day, but it was too little too late for the visitors.