The 26-year-old held his nerve from 12 yards after Abdul Osman was penalised for handball in the 34th minute, and that proved the difference at Firhill Stadium.
Aberdeen have now won three of their last four Premiership matches 1-0 and they remain in fifth, four points off Celtic at the top.
Partick goalkeeper Paul Gallacher denied Rooney with a save low to his left, but the Aberdeen man would not be denied soon after.
Collum judged that Osman had handled in the penalty area from a corner and Rooney fired the resulting spot kick low past Gallacher, the hosts feeling doubly hard done by as they felt David Goodwillie was offside in the build-up to the corner.
There were fewer chances after the break, although the impressive Gallacher denied Rooney a second in the 73rd minute when he got down well to keep out the former Birmingham City man's powerful header.
