The victory was Stewart's second in a row, second of the season and 31st of his Nextel Cup career.
Reed Sorenson was on the pole for the 160 laps around the 2-1/2-mile Indianapolis Motor Speedway.
Stewart built the lead to 0.964 seconds with eight to go and 1.347 seconds one lap later. He continued to build the lead and then cruised to the checkered flag unchallenged.
The next race is set for next Sunday at the Pocono Raceway.
Celebrity Families of 2014 [PHOTOS]