The champions dominated throughout and claimed all three points thanks to a Callum Paterson effort and second-half strikes from Wilson and Soufian El Hassnaoui.
Robbie Neilson made seven changes for the visit of Alloa, who had Paddy Connolly in the dugout once again as new manager Danny Lennon waits to take charge of his first game.
The away side enjoyed good early possession against the much-changed hosts but Hearts had a mild appeal for a penalty waved away in the seventh minute when Sam Nicholson’s shot was blocked, with referee Andrew Dallas dismissing claims for a handball.
The home side came close to breaking the deadlock shortly before the half-hour mark when James Keatings got on the end of Wilson’s cutback, but his effort came back off the post.
Morgaro Gomis then tested Alloa goalkeeper Craig McDowall from distance shortly before Billy King danced his way into the visitors’ box and fired over the bar.
Hearts’ dominance paid off shortly before half time, however, when Paterson struck from long range into the bottom left corner.
They could have doubled their lead before the interval but no one could get on the end of King’s driven effort across the box.
The home side did not have to wait long after the break to add to their tally, however, when captain Wilson got on the end of a Keatings corner to power a header past McDowall after 49 minutes.
The goalkeeper enjoyed little respite as he had to then save from both Nicholson and Gomis.
Alloa’s Iain Flannigan nearly got one back for the visitors soon after when his long range effort had Jack Hamilton scrambling in his goal but the ball flew just wide.
However, El Hassnaoui made absolutely sure of the points for Hearts when he got on the end of Nicholson’s cutback to fire into the top corner from 20 yards after 69 minutes.
Flannigan could then only watch as his 30-yard free kick clipped the outside of the post.
There was to be more misery for Alloa, however, as Mark Docherty received his marching orders in the final minute after picking up a second yellow card for a foul on King.