The home side made a bright start and should have gone ahead straight from the kick-off as Brian McPhee found himself in acres of space at the back post but his shot went just wide.
Airdrie were applying a lot of pressure in the early stages and on 7 minutes Graeme Holmes forced Ludovic Roy into an excellent reflex save following a snap shot just inside the box. A minute later Roy was again called upon, this time to turn a Gary Twigg header around the post. It seemed to be the old story for the home support as yet again Airdrie failed to capitalise on some prolonged pressure.
As the visitors began to come back into the match they should have took the lead when Bobby Mann rose above the defence to head a Gavin Swankie corner just over.
Then on 25 minutes came the pivotal point in the match when Swankie was put through on goal by Alex Rae and just as he was about to pull the trigger he was fouled by Neil McGowan. Referee Willie Collum was given no option but to show the left-back a straight red card and from the resulting penalty Lyle made no mistake in putting Dundee ahead.
Into the second-half Airdrie were again the more dominant side and should have got back on level terms when Stephen McDougall played Twigg through on goal and his shot could only be parried by Roy but he blasted over from the rebound.
The visitors should have wrapped the game up on 58 minutes when Greg Strong saw his shot rebound back off the post following a Swankie free-kick.
For much of the second-half Airdrie pressed for the equaliser and went close through McDougall and Holmes before Kevin Christie saw a shot hit the side-netting in the dying minutes, but it was to no avail as Dundee held firm for the points.