Winning at the Belle Isle Street Circuit was always going to be a challenge for Power who started the race in 16th.
However, with Team Penske opting for a two-stop strategy, the 41-year-old Australian was able to gain the necessary track position on what was a bumpy and narrow track.
Power completed the final 20 laps on Firestone alternate 'red' tyres, which provide more grip but rapidly lose traction. Rossi, on the other hand, was on the far more durable primary 'black' tyres as he looked to challenge for the win.
The Aussie left the pit lane for the final time on Lap 51 of 70, with a lead of 16.079 seconds over Rossi.
The American trimmed that lead to 12.128 seconds with 10 laps remaining, and realistically needed a late caution period in order to stand a serious chance of an overtake.
That didn't happen, but Rossi was handed a late lifeline as Power found himself stuck behind Jack Harvey with eight laps to go. Considering the fragility of his tyres, the Aussie decided against an overtake and stayed behind the Englishman.
Rossi put his foot firmly on the gas and cut Power's lead to 6.5 seconds with three laps to go.
Ultimately, the challenger ran out of laps as he finished the race an agonising 1.8 seconds behind.
When asked about tyre preservation, Power said: "I drove it as straight as I could. I never put any slip (angle) into it.
"I was just driving it really straight and really nice on the brakes and the throttle. I knew if I could keep a reasonable gap until the end, we'd be OK."
Looking back at his challenge, Rossi said: "I think one more lap would have been really interesting. But you've got to give credit to the 12 guys and Will. That's hard to do at the end, to hang on. It was a good recovery from yesterday. The strategy was good."
This was the 41st career victory for Power, but first in almost a year with his last triumph coming at the Indianapolis Motor Speedway back in August 2021.
The attention will now turn to next weekend's Sonsio Grand Prix at Road America.