The Bully Wee, chasing a fourth successive win, started on the front foot and Chris Smith had a header diverted onto a post by Annan ’keeper Jordan Hart.
Sean Higgins, two-goal hero at East Stirlingshire last Saturday, went off injured and was replaced Jamie Watson whose first contribution was to set up Clyde’s opener five minutes before the break.
Watson played in David Gorrmley who beat Hart with a firm low drive.
Clyde doubled their lead three minutes into the second period when Jon Paul McGovern rammed a ferocious strike in off the bar to grab his first goal for the club.
Annan, needing a win to move level on points with Clyde and boost their own promotion hopes, pulled a goal back 12 minutes from time when Matty Flynn netted from Smart Osadolor’s set-up.
But Clyde held on and - with four wins on the trot and just one defeat in the last nine games - appear to be running into form just at the right time.
Next up for Barry Ferguson’s side is another home match with Arbroath on Saturday.