Blackburn boss Tony Mowbray was defiant following the 3-2 defeat at West Brom last Saturday, and in driving rain his side started on the front foot here.
Jayden Fevrier went close early on after cutting on his left foot and bending a shot narrowly wide, and Dapo Afolayan also fired off-target as the hosts threatened an opener.
Hayden Carter came within inches of breaking the deadlock when his stabbed effort from Todd Cantwell’s corner hit the inside of the post and rolled across the line – but moments before the break Gudjohnsen struck.
And the opening goal was a soft one from Wrexham’s point of view as Patterson failed to deal with Morsy’s tame effort and Gudjohnsen made no mistake from the rebound.
The visitors were uninspired for 45 minutes – their best chance coming when Moore headed tamely over – and needed Patterson to partially make amends after the break as he denied Afolayan with his feet.
But Phil Parkinson’s men finally responded and Sam Smith nearly levelled when he glanced a header wide from Callum O’Hare’s cross.
They went closer still when Moore’s goal-bound effort was blocked by Carter and Joe Morrell blasted the loose ball inches past the post.
But with the home crowd braced for a tense finale, the impressive Cantwell found Gudjohnsen and the club’s top scorer finished clinically from close range.
Parkinson immediately sent on Ollie Rathbone, Danny Imray and Ryan Longman in a bid for a late comeback, but it was Blackburn who made it three successive wins at Ewood Park for the first time since October 2024.