Scottish Championship side Livi have yet to win the league this season, but a goal in each half from Andrew Barrowman and substitute Kyle Wilkie was enough to see off their Scottish League One opponents.
Livi broke the deadlock in the 38th minute when midfielder Martin Scott supplied the decisive pass for Barrowman, who tucked home a neat right-footed finish.
The visitors' defender Jason Talbot's header flashed wide of the target just before half-time, but Aidrie continued to hold their own after the break.
Wilkie showed fine control while off balance just inside the penalty area to steer home the decisive second goal in the 67th minute.
Airdrie midfielder Davie Sinclair spurned a good chance to pull one back five minutes later, but Livi's defence held firm.