It was the Bully Wee's eighth win in 11 games and moves Danny's Lennon to within five points of a promotion play-off spot.
Kevin Nicoll - scorer in Saturday's draw at Annan - was on target again, the skipper making the breakthrough in 21 minutes with a header from a Chris McStay corner.
Five minutes later Jack Boyle doubled the visitors' advantage with a fine finish from the edge of the box.
City came from two down to level in the sides' last meeting at Broadwood before Clyde grabbed a last-minute winner.
But David Goodwillie made sure there would be no repeat five minutes after the break, netting from a tight angle to take his season's tally to 23 and put the result beyond doubt.
However the shine was slightly taken off the win when Nicoll was sent off near the end for a second yellow card near the end.
Next up for Clyde on Saturday is a home match against leaders Montrose.