They entered the 33-car field on a day that Firestone engineers estimated the track temperature at the Indianapolis Motor Speedway was 73 degrees.
The 93rd Indy 500 will be run at the Brickyard's 2.5 mile oval track next Sunday.
The Indianapolis Star reported Andretti earned a spot in his 10th Indianapolis 500 by posting a four-lap average speed of 221.316 miles per hour during his third qualifying attempt.
Earlier, he was passed by re-qualifiers Nelson Philippe and Milka Duno and bumped by Bruno Junqueira.
"I tell you, a couple years ago, I made the Daytona 500, and we shouldn't have or we weren't expected to," Andretti said at news conference.
Helio Castroneves won the pole last weekend and is joined in the front row by Penske Racing teammate, Ryan Briscoe and Chip Ganassi Racing's Dario Franchitti.
Swim Week Miami Beach 2014 [PHOTOS]