The Belgium midfielder, introduced at the start of the second half, fired Boro 2-1 ahead on 69 minutes before fellow substitute Malaury Martin put the game out of reach with a third.
Adam Rooney had given Birmingham the lead from the penalty spot, only for Barry Robson to level just after the restart.
The victory means Boro continue their unbeaten start to the season with their third consecutive three-point haul.
Nathan Redmond had the first effort of the match but his shot from distance fizzed just past the post.
The home side started to come back into the game and it took a smart save from Boaz Myhill to prevent Robson giving the hosts the lead with a drive from 20 yards.
Rooney, recalled to the side after sitting out his side's goalless draw with Nacional in the Europa League, was close to an opener after 13 minutes but Chris Burke's low cross just evaded the striker's outstretched leg.
After Scott McDonald was fed neatly by strike partner Marvin Emnes, the Australian striker failed to direct his shot on target before seeing another effort well saved by Myhill.
Myhill was continued to be tested as Boro started to dominate, this time producing a smart save from a deflected Emnes strike.
Tony McMahon, back in the Boro side after a one-match suspension following his red card against Leeds last week, almost broke the deadlock but - from a tight angle - fired his shot against the post.
Against the run of play, Birmingham took the lead after 36 minutes from the penalty spot. Rooney fired into the bottom left corner after the lively Burke had been brought down in the box.
Boro almost responded immediately but, after turning in the box, Julio Arca fired a weak shot straight at Myhill.
The home side did equalise three minutes after the restart when Robson's free-kick crept in off the near post.
Rooney could have fired Birmingham ahead for the second time but he failed to hit the target before Middlesbrough secured the victory with two goals in three minutes.
After replacing McDonald, Haroun made an instant impact and, after having a shot blocked, he netted the second goal by slotting in from 12 yards, before Martin drilled home from 25 yards.
Jean Beausejour almost grabbed a consolation in stoppage time but his effort from distance was easily saved by Carl Ikeme.