The match was the rescheduled tie between the two clubs after Hamilton player Ross McCabe suffered a heart attack on the pitch in the previous encounter nearly losing his life.
The tie was barely in its infancy when Richard Offiong struck with his first goal of the night.
The gangly striker picked the ball up on the right wing and proceeded to nonchalantly waltz his way around the Clyde defence before cutting inside and finishing in the most confident of manners with the outside of his right boot.
The game was played at a brisk pace in the first half with a lot of physical action that threatened to spill over into something more serious, with Dougie Imrie the most likely offender.
Accies doubled their lead through the in-form Offiong on the half-hour mark as the away defence struggled to cope with the aerial power of Mark McLaughlin.
Tony Stevenson swung in a right-foot free kick that McLaughlin met with power. The ball was nodded in the direction of Offiong who displayed a deft touch to nod the ball over the stranded Peter Cherrie.
The Hamilton faithfully barely had a chance to park their rears back on their seats before the Bully Wee had pulled a goal back.
An adjudged hand ball presented Steven Masterton with a free-kick 20 yards from goal. The midfielder curled a spectacular effort into the top corner past the bemused Raymond Jellema.
Accies were not to be outdone and quickly grabbed their third of the match two minutes later.
Offiong bundled through the away defence once more and the loose ball fell to David Winters. The former Ross County player nudged the ball to Mark Gilhaney who slipped his shot past Cherrie from an acute angle.
The second half developed into a dreary stalemate among the midst of a serious downpour from the heavens, with the best chance of the half falling to Masterton, who could only watch in anguish as his 20-yard free-kick was superbly parried by Jellema.