Not surprisingly Bully Wee boss Danny Lennon stuck with the same side who had beaten Falkirk the previous Saturday.
Montrose had won both previous meetings between the sides and the Gable Endies had an early chance when Martin McNiff was put under pressure following a pass from David Mitchell.
The Clyde man lost the ball but Mitchell deflected the shot from Blair Lyons behind and, from the resultant corner, did well again to keep out a powerful Andrew Steeves strike.
And, after Chris McStay had a decent long-range strike well saved by Greg Fleming, it was Clyde who took the lead in the 12th minute.
Adam Livingstone picked out Chris McStay with a cross to the far post and the Clyde midfielder headed the ball back across goal for Ally Love to turn home from close range.
The home goal led a charmed life a few moments later. Mitchell failed to gather a Lewis Milne free-kick but recovered to prevent Lewis Hawke netting the rebound.
Ray Grant then stopped Lyons’s follow-up effort from crossing the line and was again in position to block another follow-up strike from Steeves. Clyde then came close to doubling their lead when Ross Cunningham just failed to get on the end of David Goodwillie’s ball across the face of goal.
But the Bully Wee did get a second six minutes into the second period when Grant collected a Goodwillie pass 25 yards out and hammered a left-foot rocket wide of the diving Fleming into the corner of the net.
But Montrose hit back quickly; just two minutes later Lyons was allowed get on the end of a Milne corner to head past Mitchell from inside the six-yard box.
A fine Fleming save from Martin McNiff’s header kept Montrose in it and in a frantic finale Craig Johnston was denied by Mitchell and then had an effort blocked by Tom Lang.
But Clyde held on for a valuable three points.