Blair Henderson's early header ended Airdrie's hopes of Betfred Cup progress as Edinburgh City won 1-0 in Lanarkshire.
Henderson headed the only goal in the fifth minute when he met Sam Newman's cross.
Thomas Robert missed some first-half chances for the hosts and came close to a second-half equaliser with a spectacular volley.
Airdrie could not convert a series of late chances as they remained on three points ahead of their trip to face Group H leaders Livingston on Saturday.
