Ex-Wrexham player Neil Wainwright sank his old club by setting up both goals.
He put over a left-wing cross for Barry Conlon to head home and then curled a superb free-kick into the six-yard box for Craig Liddle to finish with a powerful header.
Wrexham had a poor game and seldom looked lightly to score. Lee Trundle gave goalkeeper Andy Collett an easy save, tipping a left-wing shot over the angle of the bar and post and another shot from the Wrexham striker was blocked on the line.
Collett saved again when Lee Jones tested him with a looping header in the second half.
Darlington had the better of early play and Ian Clark fired a shot over the bar, then missed an open goal when he blazed over from close range.
He was out of luck again on the stroke of half time when he hit the bar after Wrexham keeper Paul Whitfield had blocked a shot from Richard Hodgson and pushed it into his path.
After Conlon had opened the scoring, Clark was through again this time to be foiled by another Whitfield save and when Wainwright tried a long-range drive the Wrexham boss Denis Smith was bitterly disappointed.
He said: "We have gone out without even a whimper. They beat us with good honest football. I am unhappy with the whole performance.
"This is the FA Cup after all and if you're going to go down, then go out with a bit of passion and fight." A delighted Darlington manager Mick Tait said his match plan had worked to perfection: "It was a great result and we performed right from the start. We had a plan to stop them playing, but we had to make sure we didn't just stifle things.
"We made a lot of chances and deserved to win." On speculation that he might be promoted from caretaker boss to get the job full time on a permanent footing: "I haven't spoken to the chairman yet, I just want to make sure the club is right for the future."