Early goals from Reda Johnson and Chris Lines put Wednesday in control, and although substitute Ian Goodison pulled a goal back for the visitors, it was too little too late.
Wednesday took the lead in the second minute when Lines crossed from the left wing, after Ben Marshall's free-kick was blocked by the defensive wall, and Johnson found the net with a firm header.
It was 2-0 five minutes later when Jon Otsemobor passed to the unmarked Lines, who beat Paul Rachubka with a low shot.
Wednesday had a good chance to go further ahead when Clinton Morrison's shot was parried by Rachubka and Chris O'Grady shot wide from the rebound with the keeper off his line. After the restart, Marshall had a shot turned wide by Rachubka and then Wednesday keeper Nicky Weaver kept out a shot from Lucas Akins.
Goodison headed in a cross from Danny Holmes to reduce the arrears with eight minutes remaining, but Tranmere were unable to force an equaliser.