Ellison joined City on loan from Rotherham in midweek, with Omar Daley moving in the opposite direction and his goal secured a first win in seven attempts to lift the pressure off former Wycombe boss Peter Taylor.
Ellison arrived at the far post to apply the finish after Michael Flynn's throw was drilled to the far post by Luke O'Brien. The scorer was booked for removing his shirt in celebration.
Taylor also handed a debut to striker Scott Dobie, on loan from St Johnstone.
O'Brien made a goal-line clearance to prevent Chris Westwood giving Wycombe a 16th-minute lead and three minutes later Bradford lost striker James Hanson to injury.
Bradford goalkeeper Lenny Pidgley made an acrobatic save from Stuart Lewis to keep the first half goalless but after Ellison had struck the vital blow, promotion chasers Wycombe should have equalised when substitute Matt McClure somehow headed over the bar from eight yards.