Aaron Burns scored twice as Linfield made it back-to-back wins in the Irish Premiership with victory at Dixon Park.
Burns got the first on six minutes from Matthew Tipton's ball in from the left.
Ards levelled 10 minutes later through a James Cully penalty after Craig McMillen was fouled by Sean Ward.
Tipton restored Linfield's lead in the 69th minute by heading in from Michael Carvill's cross and then Burns headed in from close-range after Carvill's corner from the left.
After taking just one from their first four fixtures, Linfield have beaten last season's promoted teams away - Warrenpoint Town and Ards.
The victory takes David Jeffrey's Blues up to eighth place in the Irish Premiership table with Ards remaining bottom.