It was the first career IndyCar Series win for the four-year veteran, who drives the No. 6 Team Penske Dallara Honda.
Dixon was dominating the race when he led Helio Castroneves, Briscoe, Dan Wheldon and Tony Kanaan with 85 laps remaining, but Briscoe started a late climb by passing Penske teammate Castroneves with 65 laps left to take over second place.
Briscoe got lucky when Dixon came off pit road and settled behind him.
All that was left in the closing 17 laps was holding off a charging Dixon, and Briscoe fought off each Dixon attempt.
"It's been 30 years since Roger (Penske's) first IndyCar win," Briscoe told RACER magazine. "I can't tell you how important it is to get my first IndyCar victory for him in this race."
Kanaan, Wheldon and Castroneves completed the top-five.