Hard-working Boro see off Wednesday to move top of the Championship
The visitors went into the game looking to bounce back from their disappointing defeat to Nottingham Fores ton home turf before the international break and were the better side for the first 45 minutes, though it was the hosts who came closest to scoring as Adam Reach's flicked header from a Barry Bannan cross grazed the crossbar on its way over.
However, Tony Pulis' men stepped their energy and intensity levels up a notch after the break, finding the breakthrough just four minutes after the restart.
Assombalonga did well to battle under a long ball down the right, before Jonny Howson found the evergreen Stewart Downing. The former England winger had the presence of mind to wait for support and send Howson in behind with a lovely backheel. The former Norwich man got his head up and pulled the ball back for Besic, who was excellent in the second half, with the Bosnian duly finding a yard of space and drilling low into the far corner beyond Cameron Dawson.
The lead was doubled just minutes later and it came gift-wrapped on this occasion, Tom Lees getting caught in two minds and surrendering possesion to Besic, who strode forward into the open space before drawing Dawson and squaring to give Assombalonga the most simple of finishes into an unguarded net.
The introduction of giant Kosovan international Atdhe Nuhiu was always likely to cause Middlesbrough problems and so it proved as the hosts took a more direct route to goal, with Aden Flint having to be alert to hack away his goal-bound header.
The in-form Adam Reach drew the 'Owls' back into the game with eight minutes to goal as he continued his streak of spectacular goals by volleying right-footed into the far corner past a static Darren Randolph when the away side failed to clear a corner.
That was Wednesday's first shot on target of the game, but the managed to apply some pressure in the dying stages and there was still time for some late drama as an incredible goal-mouth scramble ended with bodies strewn across the Hillsborough turf, but Middlesbrough held on for a deserved victory to move back top of the Championship ahead of Saturday's games.