Power started ninth but took the lead on a late caution and pulled back in front of Dixon on the double-file restart with 16 laps left Sunday at Barber Motorsports Park. It was the second straight win for Chevrolet and Team Penske, which is also 3 for 3 in the Alabama race.
Power and Dixon pulled away from the field for a 1-2 finish, just like a year ago. St. Petersburg winner and pole-sitter Helio Castroneves of Penske edged Graham Rahal for third.
Power had his fast qualifying time in the second session negated because a caution came down during his run, forcing the Australian out of his more familiar front-runner status at Barber, where he had held the pole the past two years. He still managed to work his way toward the front, moving into the top five by passing Tony Kanaan on the hairpin fifth turn a third of the way through.
This time, the restart provided the last real drama up front after a caution when Katherine Legge went into a gravel pit.
Power disproved his own theory that it would be tough for anybody opening outside the top four to win on a course that typically has featured infrequent passing, making up ground with the help of tire strategy and swift work on pit road.
Then again, Power consistently had the fastest car in practice and qualifying here before the poor timing of a day earlier. It was a nice rebound also from a St. Petersburg performance he called "the worst race of my life."
It was another tantalizingly close call for Dixon, who has been runner-up in the season's first two races and all three years at the tree-lined 2.38-mile road course in suburban Birmingham. Dixon couldn't muster much of a challenge in the final laps, finishing 3.37 seconds behind.
Rahal couldn't find a way past Castroneves, the 2010 winner.
The focus returned to racing after the emotional weekend in St. Petersburg, the adopted hometown of Dan Wheldon and the first race since Wheldon's fatal crash in October's season finale. Power matched Wheldon's 16 career wins in Indy cars, 14 of them coming on road or street courses.
The race provided significantly more maneuvering after Power led from wire to wire in 2011. Dixon beat Castroneves and James Hinchcliffe out of pit road on the first stop to move up front but lost precious time and the lead on the second.
Rookie Simon Pagenaud was fifth.
Formula One veteran Rubens Barrichello had a strong performance in his second IndyCar race, finishing eighth. Defending series champion Dario Franchitti moved up eight spots after a rough qualifying session and was 10th, still a slow start by the standards of Dixon's Target Chip Ganassi teammate.
The new cars' safety measures still haven't been put to the test by the first two races. There was some attrition starting moments after the race began.
Lotus cars had a mixed performance. Alex Tagliani didn't make it through the first lap before mechanical failure ended his day. Charlie Kimball went into the gravel midway through. Takuma Sato had to pull off the track on the 54th lap, climbing out and walking down the grass back to pit road.