The Chip Ganassi Racing driver qualified 22nd, but recovered to claim a win at the circuit for the fifth time in the past eight years.
Dixon led 45 of the 90 laps and was aided by a three-stop strategy as he finished ahead of Sebastien Bourdais (KVSH Racing) and James Hinchcliffe (Andretti Autosport).
The win was the New Zealander's first of the season as he remained sixth in the championship standings.
Will Power was sixth on Sunday, but the Australian Team Penske driver regained the lead in the drivers' standings.
Power (548 points) is ahead of team-mate Helio Castroneves (544) after the Brazilian ended up 19th.
Ryan Hunter-Reay (485 points), Simon Pagenaud (484) and Juan Pablo Montoya (447) are the other drivers ahead of Dixon (440).