Mark Reynolds' late winner over Kilmarnock handed Aberdeen a fourth straight away win and lifted them into second place in the Premiership.
The centre-back made a decisive run and leap to meet Niall McGinn's 82nd-minute corner and head home from six yards to move the Dons above his former club, Motherwell, whose game against Inverness was postponed on Saturday.
The Dons dominated after half-time, although both goalkeepers made two good saves in the second half, and they were thankful for a dubious decision that robbed Kris Boyd of a goal during a first half that Kilmarnock largely controlled.
Dons substitute Nicky Low was shown a straight red card for a two-footed, stoppage-time lunge on Clohessy, but Aberdeen were never in danger of losing a grip on the three points in the remaining seconds.