Cowdenbeath boss Jimmy Nicholl greeted his side’s League Cup injury-time victory with relief more than delight.
The Blue Brazil went into the first round clash having been dumped out of the Petrofac Cup by lower league opposition a week earlier.
And a similar embarrassing outcome looked on the cards when David Gray fired the Bully Wee in front midway through the first half.
The League Two side held their advantage until six minutes after the restart when Lewis Milne’s spectacular long-range strike flew past Jamie Barclay.
Both sides had chances to win it but the game looked to be heading for extra time until Kyle Miller pounced to send the Fifers through with seconds remaining.
Nicholl admitted: “They counter-attacked us a couple of times and my heart was in my mouth but thankfully we got there and I’m glad we’re still in the draw.
“I thought we played well in the first half. Clyde are a decent side, they build from the back and are useful up front so we knew that it was going to be a tough one for us today.
“We didn’t particularly play well last week against Brechin and we went out, so we were hoping to make amends for last week.”
Nicholl, though, admitted his side had to dig deep following the shock of going behind.
He added: “We had a few opportunities first half, and then the lad came up with a wonder goal just before half-time which was a bit of a setback.
“But I wasn’t going to rip into the players at half-time as we were still in the game and it took another wonder strike by Lewis Milne for the equaliser and there was good energy at the end from Kyle Miller.
“It wasn’t easy and we had a fright a couple of times.”
Bully Wee boss Barry Ferguson admitted: “Losing the late goal was a kick in the teeth.”