Helio Castroneves was second to make it a 1-2 finish for team owner Roger Penske.
Montoya won for the first time in the CART/IndyCar Series since 2000 and had his first major victory since he won a road course race at Watkins Glen in NASCAR in 2010.
With double points awarded in the 500-mile races, Castroneves moved into a tie for the points lead with
Power was hit with a blocking penalty on Castroneves late in the race and had to serve a drive through penalty, costing him a shot at racing for the win. He finished 10th.
Carlos Munoz, Ryan Briscoe and Scott Dixon completed the top five.
Montoya, who won from the pole, took the lead for good when Tony Kanaan was forced to pit for fuel with four laps left. Montoya took it from there and continued to stamp himself a player in the championship hunt.
"As soon as we signed him, I knew he would be an asset for us, and a headache," Castroneves said.
Montoya damaged his front wing when he connected with Power on a pass for the lead on the 167th lap. Power's penalty troubles continued at Pocono when he blocked Castroneves on the 171st lap, effectively ending his shot at victory.
Montoya, the 1999 CART champion and 2000
Montoya wanted a competitive ride again after lackluster results driving for Chip Ganassi in NASCAR. He knew his open wheel return would have a learning curve: Montoya last ran in CART in 2000, then left Formula One midway through the 2006 season for NASCAR.
After only two top 10s in his first seven starts, Montoya reeled off a third, second and seventh in his past three. Now, he has a win needed to validate his open wheel comeback.
"Are you kidding? This guy is unbelievable," Castroneves said. "Coming back after 15 years to win a race, he did a great job."
The 200-lap race was caution free for the first 158 laps until Graham Rahal spun to bring out the yellow. The 158 consecutive laps of green flag racing to open a race was the longest stretch for a 500-mile race in IndyCar history.
Indianapolis 500 champion Ryan Hunter-Reay lost his shot at winning the series' Triple Crown when he was forced out only 28 laps into the race. Pocono and Fontana join the Indianapolis 500 as the three races that use three-wide starts, run 500 miles and award double points.
Hunter-Reay threw his hands up in frustration when he left a car that had a suspension issue.
"It just gave up," he said.
He would rejoin the race and finished 18th.
Carlos Heurtas, a winner last weekend at Houston, also left the race when his car wouldn't start on pit road.
Rookie Jack Hawksworth missed the race and was hospitalized with a heart contusion suffered Saturday in an accident during the second practice session.
Montoya won the race in front of a crowd estimated at much less than the 35,000 that attended last year.