Forfar are the only side to beat Ally McCoist's side this season after they won their League Cup tie at Station Park in August.
But there was to be no repeat performance in Scottish League One, with Lee Wallace and captain Lee McCulloch also on target after Gavin Swankie had earlier equalised Clark's opener.
Wallace made the opening goal, with Clark getting on the end of his cross to head past Loons goalkeeper Darren Hill.
Hill did well to keep out an angled drive from Fraser Aird and Forfar were soon back on level terms, Swankie firing in a shot from distance that left Rangers keeper Cammy Bell with no chance.
But that was as good as it got for the visitors, who found themselves 4-1 down at the interval.
Clark notched his second of the night when his deflected effort came off the hapless Darren Dods before Wallace cut inside from the left to fizz a low drive into the bottom corner from the edge of the box.
Hill pulled off a superb save to deny Clark his hat-trick but he secured his treble before the break when he scored from close range after Ian Black's 35-yard shot came back off the crossbar to allow him to slot home.
Rangers continued to push for further goals in the second period and Bilel Mohsni's header skimmed off the bar just two minutes after the restart.
Instead it was left to Clark to add the next goal, although Mohsni played his part as he headed Aird's corner into the goalmouth for Clark to score from close-range.
McCulloch missed a penalty at the weekend but he made no mistake in dispatching his latest effort after David Templeton had been fouled in the area.
There was an added boost for Rangers fans when Dean Shiels came off the bench to make his first appearance since August after battling back from a long-term knee injury.