Ronan Darcy came extremely close to scoring early on for Wanderers, after good build up play.
The forward hit a shot towards the top corner, only for goalkeeper Bagan to make a great save.
Both Connor Hall and Harry Brockbank both had powerful headers at goal, with Halls able to clear them off the line.
The Bluebirds took the lead through Faniyan, as the Cardiff player headed home from a Cameron Coxe cross.
Wanderers did have a goal disallowed soon after, as Tanimowo had been judged to be offside
Cardiff doubled their lead just past the half hour mark, with Moor firing through the legs of Wanderers shot stopper James Aspinall.
Moving into the second half and the home side remained the aggressor between the sides.
With 13 minutes of time left, a fantastic solo goal from Ward made it 3-0 to the Bluebirds.
In an almost instantaneous response, a Joe Muscatt high quality cross into the area found Harry Brockbank who got on the end of it to pull one back for Wanderers.
Connor Hall then got in front of the defender to score from a cross by Brockbank from close range, to put immediate pressure back on Cardiff.
Ronan Darcy had a great opportunity to equalise, but chose the wrong option in the end and the chance was squandered.
We kept pressing right up to the final whistle, but unfortunately time was against David Lee's men.
Wanderers XI: Aspinall, Brockbank, Muscatt, Senior, Hartshorne, Earing, Graham, Hall, Tanimowo, Brown, Darcy.
Substitutes: White, B. Williams, Richards.