The visitors survived an early scare when keeper Peter Cherrie was ruled to have caught the ball outside his penalty area but Kevin McDonald's free kick was aimed straight at the wall.
Home goalkeeper Stephen Robertson was then rather fortunate as he looked on casually while Stephen O'Donnell hit the top of the crossbar with an angled free kick.
Airdie dominated the rest of the first half although Clyde were their own worst enemy with Cherrie losing concentration once again and almost gifting the opening goal to Gary Twigg.
Fullback Eddie Malone also came desparately close to heading the ball into his own net but Cherrie managed to regain his composure in time to make a useful save from McDonald shortly before half time.
Cherrie had little chance within five minutes of the restart when Frenchman, Xavier Barrau gave Airdrie the lead with an ugly, but effective, finish which deflected off his shoulder.
Clyde's reply was immediate, after Malone's free kick forced a wonder save from Robertson, O'Donnell equalised with a curling right-foot shot from 12 yards.
Airdrie upped their game and Cherrie dived to his right to push away a long-range free kick by Barrau before veteran Brian McPhee headed fractionally wide.
Moments later, McDonald's low drive from the edge of the box made it 2-1 although the visitors kept pressing to the very end in pursuit of another equaliser.