Joel Thomas' goal put Hamilton in control at New Douglas Park
Two late goals sent Hamilton into the third round of the Co-operative Insurance Cup at Clyde's expense.
Hamilton went after 17 minutes when James Grady headed home.
Pat Clarke drove in the equaliser off the inside of the post three minutes later, but Clyde had Michael Ohnesorge was sent off after 66 minutes.
Joel Thomas' shot slipped under goalkeeper Peter Cherrie 16 minutes later and Tony Stevenson secured the win with a last-minute penalty.
Hamilton were forced to work hard for their victory over the First Division side, with the scoreline doing little to reflect the action.
Accies skipper Alex Neil and Mark McLaughlin both suffered injuries at the weekend, forcing boss Billy Reid to change his side for the first time this season.
The home side claimed the best of the chances early on, with Simon Mensing connecting well with a Sebastian Sorsa cross from the right only to see his point-blank header comfortably held by Cherrie.
David Elebert then nodded narrowly past the upright, with the header taking a deflection off Ruari MacLennan after Stevenson had sent a teasing flag-kick into a packed goalmouth.
What had been a fairly dreary tie suddenly burst into life with 17 minutes gone when the home side opened the scoring.
James McCarthy started the move, playing the ball to Sorsa on the by-line.
His cutback was met by Grady and the diminutive striker did well to direct a header past Cherrie from six yards.
The celebrations were short-lived, however, and Clyde restored parity when the ball broke 25 yards out to Clarke, who drilled a low shot in off goalkeeper Tomas Cerny's left-hand post and into the back of the net.
Grady attempted to help himself to another goal for Accies with a well-struck shot from the edge of the area, but the effort cannoned off the body of Mark Brown and the Bully Wee were able to clear the danger.
At the other end, a ferocious long-ranger from Billy Gibson was cleared off the line by Chris Swailes with the keeper helpless before Stuart Kettlewell blasted the rebound well over the crossbar.
Thomas replaced Grady after an hour and was unfortunate not to grab a goal of his own when he met Stevenson's corner with a glancing header that fell across goal and wide of target.
Clyde's hopes were dealt a blow when they were reduced to 10 men with 24 minutes to go when Ohwesorge picked up a second yellow card for a crunching tackle on Brian Easton.
As expected, Accies piled forward in search of the winner and Thomas was not too far away with a thunderous drive that rattled the crossbar before Stevenson sent a free-kick whistling inches wide of the post.
The impressive Thomas did claim a goal, unleashing a long, low shot that slipped under the goalkeeper's body to leave the net bulging with 10 minutes to go.
The tie was already over as a contest when Lucas Akins was felled by Cherrie in the box and Stevenson converted from 12 yards.
Hamilton manager Billy Reid:
"Obviously I'm delighted because we are an SPL club now and, if Clyde had won, it would have been an upset.
"We warned the players and told them there probably would be an upset in one of the ties - we just had to make sure it wasn't us.
"We weren't at our best tonight and all credit to Clyde, they put us under a wee bit of pressure but I thought we deserved to win the game.
"The important thing for me is that we won the match and I think we deserve to be in the next round."
Clyde manager John Brown:
"The boy knew if he was clumsy that it could go either way. It was disapointing. Maybe the ref could have had a word with him. But referees have a hard enough job.
"We created a number of chances but, when it went to 10 men, it was always going to be a battle.
"For effort, I've never faulted the players this season and if they continue like that, they will pick up points in the league.
"I felt for them tonight though - they put in a lot of effort and there wasn't a great deal between the two sides."
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