The livewire frontman, on loan from Ipswich Town, opened the scoring on 32 minutes when he was first to react after a shot from team-mate Franz Burgmeier was deflected.
Clarke nipped in to lift the ball over keeper Kenny Arthur.
The goal came with Darlington down to ten men, as Clarke's strike partner Liam Hatch was off the field having stitches put in a cut head.
Once Darlington were back to the full complement they took total control. Clarke lobbed his second goal on 53 minutes after racing on to a pass from skipper Steve Foster.
And Darlington wrapped up the win when Alan White scored his first of the season with a powerful 76th minute header from an inch-perfect corner from Burgmeier.
The closest Accrington came was on 65 minutes when Paul Mullin stretched to reach a corner from John Miles, but his effort was blocked on the line by Darlo keeper Simon Brown.
However, before Darlington had opened the scoring Jimmy Ryan went close for Accrington with a dipping long-range shot which brought a superb save out of Brown.
Soon afterwards Ryan might have scored but he fired wide after Mullin set up a good opening for him.
However in the end Accrington were well beaten with Clarke in particular proving too hot for them to handle.
He was a threat every time he had the ball and was always looking to get behind the defence whenever Darlington came forward.
The home side were solid in defence and with Burgmeier providing some quality crossing, Darlington could have won even more convincingly against a side that has now picked up only one point out of 12.