The Dons were a man down for more than an hour after Mark Reynolds' dismissal in the 26th minute and within seconds of that Ian McShane had put the Dingwall side ahead.
WATCH DEREK MCINNES' POST MATCH INTERVIEW
But Adam Rooney levelled before a brace from Shay Logan gave the Dons a 3-1 cushion, and although McShane pulled one back the visitors held on to keep the pressure on Scottish Premiership leaders Celtic.
McInnes said: "I thought we played a lot of good stuff - our initial start to the game was excellent, it was one-way traffic. I don't think [Aberdeen goalkeeper] Scott Brown touched the ball in the first 10, 15 minutes.
"The response was excellent from the players to go 2-1 up - it gave us something to hold on to.
"I thought we were comfortable for the majority of the second half. The third goal said everything - my left-back, who is high up the park, crossing for my right-back to score."
Source: Sky Sports