The early stages saw both sides force early corners with Simon Mensing heading over for the home side from Darren Sheridan's kick.
The visitors had an effort from Owen Coyle blocked by John Potter and a Martin Hardie shot slid wide of the left hand post.
Airdrie's Mark McGeown was the first keeper to be called into action in the 24th minute when he atoned from his initial error to block point blank from Eddie Malone.
After 33 minutes the keeper again had to be on his toes to save from another Malone effort at his near post.
The remainder of the half was notable only for a flurry of bookings, with Gary Bollan and Malone cautioned for the home side and Paul Lovering for the visitors.
Airdrie started the second half the brighter of the two sides with home keeper Bryn Halliwell in action to keep out a deflected Alan Gow effort before making an excellent block from a Mark Roberts effort.
On the hour mark William McLaren's cross was met sweetly by Coyle, but his effort rebounded off Bollan's face.
At the other end the McGeown had to look sharp as Malone looked to have latched onto Mensing's long ball, but the keeper won the race and smothered the danger.
As the Diamonds pushed for the elusive goal they were caught with a sucker-punch after 78 minutes, when Mark Gilhaney's cross was half cleared to Jones at the edge of the box - and the debutant hit a powerful right-foot shot that left McGeown helpless.
Clyde held out for what was an unlikely victory given the way the second half had gone.