Dixon crossed the finish line 3.4 seconds ahead of Power, notching his second win of the season and the 29th of his IndyCar career.
Power, the pole sitter, led the first 56 laps of the 85-lap race on the 2.258-mile, 13-turn Mid-Ohio course.
Coming in third was rookie Simon Pagenaud, while Sebastien Bourdais and James Hinchcliffe rounded out the Top 5.
With the runner-up performance, Power took a five-point lead over Ryan Hunter-Reay, who finished 24th Sunday.
Dixon, meanwhile, moved from 61 points out of first to 28.