Two first-half goals spelt defeat for Montrose as an efficient Clyde wrapped up three points.
Montrose gave as good as they got in the opening period but Clyde grabbed the lead on 20 minutes.
A throw-out from keeper Jamie Barclay sent Stuart McColm racing down the left and his cross was knocked back into the middle by Stefan McCluskey for Michael Daly to score.
Clyde made it 2-0 six minutes later. A lunge from Colin Wilson brought down McCluskey and the striker made no mistake from the spot.
Montrose had it all to do but went close on 55 minutes when Bryan Deasley drove inches wide. The Gable Endies were denied even a consolation three minutes from time when a Graham Webster shot was brilliantly saved.
Montrose caretaker manager George Shields said: “We started well in the first half but our work in the final third let us down.
“We had chances but barely made their keeper work. My players gave their all in the second half but it was clear that Clyde had more to play for than we did.
“The penalty killed us. There was no need for Colin to dive in the way he did and the goal put their tails up.
“If we had got one goal back, I am confident we would have gone on to get something out of the game. We must take things on to next week and try to finish the season as strongly as we can.”