Aberdeen recorded successive away league wins for the first time since September 2024 to move up to 10th in the Scottish Premiership and level with Kilmarnock.
Jimmy Thelin's side had lost their last two - conceding eight goals - but showed admirable resolve to claim a precious win.
Greg Kiltie and Jesper Karlsson spurned chances for each side before Stuart Armstrong found the breakthrough for Aberdeen.
The Scotland international latched onto Jesper Karlsson's deflected effort and lifted the ball beyond Tobi Oluwayemi for his first goal for the Pittodrie club.
Kiltie almost pulled one back for the visitors late on in the first half. Aberdeen failed to clear their lines and the attacker capitalised, forcing Mitov to make the stop.
Kilmarnock started the second half brighter and Robbie Deas really should have made it 1-1 but the defender smashed his shot far too high following a corner.
Moments later, the centre-back had the ball in the back of the net after Mitov failed to gather a cross but the leveller was ruled out for an offside offence.
Marcus Dackers scrambled a late chance wide of the far post as Kilmarnock searched for an equaliser that they just couldn't find.
The result leaves Kilmarnock ahead of Aberdeen in the Premiership table on goal difference.