It took less than two minutes for assistant manager Andy Millen to be shown a yellow card for a fierce challenge on United's Alan Gow.
Saints almost took an early lead when Simon Lappin's free-kick was met by John O'Neill's glancing header but Mark McGeown finger-tipped the ball round for a corner.
O'Neill tested McGeown again when he met a near-post cross from Ryan McCay only to find the alert keeper in position to hold his flick.
Airdrie's attack could not spark into action as Saints dominated, Kean having a shot deflected wide after O'Neill had neatly chested a McCay pass into the striker's path.
Gow was fortunate to escape a caution for diving as United sought to exert some pressure but Kean headed over a Hugh Murray corner as Saints finished the half in command.
United restarted with more energy and Gow was denied by Craig Hinchcliffe coming smartly off his line to smother an early chance.
It took until the 75th minute for Airdrie to produce their first shot, Owen Coyle shooting wide.
Gow's overhead kick then landed on the roof of the net before the only goal.
The impressive McCay sent a super pass down the left flank for Brian McGinty who, after cutting inside a defender, crossed for Kean to strike with his left foot from eight yards.