Power, 37, is the first Australian to ever win the race. He passed the checkered flag about three seconds before Carpenter. Power now has 34 IndyCar wins. He also won the IndyCar Grand Prix on May 12 at the same track.
"I can't describe it," Power told ESPN after the race. "I feel like collapsing. I want to cry. I couldn't stop screaming on the radio. I can't believe it."
Stefan Wilson led the race after a restart with seven laps to go. But he headed to the pits with five laps to go, giving the lead to Power. Power managed to hold off the field down the stretch to claim the victory.
The race featured seven crashes, including one which put an end to Danica Patrick's career. Patrick wrecked on the 68th lap. She spun out in turn two in her final race.
"I really don't want to be here," Patrick told reporters. "I'm pretty sad. I'm for sure very grateful for everybody and for being able to finish it up like I wanted to. It still was a lot of great moments this month. A lot of great moments this year."
Power's victory gave Team Penske a record of 17 Indy 500 victories. He also became the first drive to sweep both races at Indianapolis Motor Speedway. Power holds an unofficial champions ship after six races this season. Teammate Josef Newgarden is in second place.