Inverness were playing in their first major cup final and remained resolute during normal time against their Scottish Premier League rivals but penalty misses from Billy McKay and Greg Tansey in the shootout condemned them to defeat.
Barry Robson, Nicky Low and Scott Vernon scored Aberdeen's first three spot-kicks before Rooney fired the winning penalty to secure Aberdeen's sixth League Cup win.
"I'm absolutely ecstatic. You can see what it means to so many people," Aberdeen manager Derek McInnes told the BBC.
"It was a tight final and I thought we had the better opportunities. However, we had enough bottle and composure to score the penalties. No matter how we won it, we've won it and deserved to win it."
Aberdeen are second in the Premier League standings, 24 points behind leaders Celtic, and Inverness are fifth.
(Reporting by Sam Holden; editing by Josh Reich)
