Montrose boss Stewart Petrie hailed his side’s first half performance as the best they have played all season.
The hosts hit back from the loss of an early goal to lead 3-1 at the break.
A second half Clyde goal left the home faithful feeling edgy, but they held on for a victory which takes them third in League Two.
Petrie said: “That was a fantastic three points after two defeats.
“In the first half we were outstanding and that is as good as we have been all season. We were 3-1 up at the break and it could have been more.
“I knew there would be a reaction from Clyde and we never really got going in the second half.
“In the first half we were a joy to watch and I didn’t want the half-time whistle.
“We lost the first goal again but we came back strongly and managed to take enough of our chances to win the game.
“We could have been out of sight, but credit to Jim Chapman as he changed things around and made it a bit nervy at the end.”
Clyde took the lead on three minutes. David Goodwillie headed on and Smart Osadolor darted in to score.
Montrose levelled on 10 minutes. A header from Craig Johnston was handled by Kevin Nicol and Iain Campbell scored from the spot.
The home side took the lead on 20 minutes when a Campbell corner broke for Chris Templeman to net from close range.
Great play by the home side in 26 minutes got the ball to Graham Webster and his shot on the turn hit both posts before crossing the line.
Clyde took the game to Montrose in the second half and on 62 minutes a shot from Barry Cuddihy was blocked on the line by Campbell.
With 15 minutes left a shot from Cuddihy was well saved by Allan Fleming but Goodwillie followed up to score.