McClaren, who guided Boro to League Cup glory and the UEFA Cup final in his spell as boss of the Teessiders, was warmly received by the fans before the game.
But there were no gifts once the match kicked off as Boro battled to edge a close-fought game with a well-taken second-half goal from Nathaniel Chalobah.
Boro created the first real chance on 15 minutes after a cagey start as a neat touch by Lee Tomlin sent Danny Graham into the box, but he fired over.
After a good spell of home pressure, Derby broke out to threaten on 27 minutes when a quick ball from Patrick Bamford picked out a run to the edge of the box by Chris Martin but, as he unleashed, defender Ben Gibson came sliding in to block and the shot looped into the arms of the goalkeeper.
Boro had a half-chance on 33 minutes as Luke Williams put a low cross into a crowded Derby box and, in a scramble, Kenneth Omeruo had a stabbed shot blocked by Andre Wisdom six yards out.
The hosts then had a golden chance two minutes later as good work by Graham sent Tomlin clear to the edge of the box but, with time and space, he fired a weak shot straight at the keeper.
Derby finished the half strongly and went close on 43 minutes as Bamford squared into the box for Martin, but Omeruo arrived with a crunching tackle to block. Then, when the loose ball fell for George Thorne, he cracked in a stinging 30-yard shot that keeper Dimi Konstantopoulos palmed away.
The visitors went close soon after the restart as Bryson broke forward only to drill a 20-yard effort straight at Konstantopoulos, then Bamford headed a cross over at the far post.
And Derby went close on 62 minutes as a Bamford shot was charged down and bounced to Andre Wisdom on the edge of the box but his effort curled just outside the post.
Boro went close soon after as a Chalobah ball sent Albert Adomah racing into the box to poke just wide under pressure from defender Jake Buxton.
The deadlock was finally broken on 69 minutes as Emmanuel Ledesma cut in from the right and threaded a ball in for on-loan Chelsea midfielder Chalobah to rifle a low shot inside the far post - his first goal for the club.
Derby may have levelled on 85 minutes as Conor Sammon floated a free-kick to the far post, but a stretching Buxton poked wide.