Canadian Hinchcliffe and Australian Will Power will join Carpenter on the front row.
Carpenter became the 11th driver to earn back-to-back poles for the 500-mile race. His average speed was the fastest since 2003.
"It's awesome to do this two years in a row," Carpenter told reporters. "I was surprised last year and didn't expect to do it this year with such deep competition.
"It’s exciting, but after going through this last year and not winning the race I’ve been so much more determined."
He led the 2013 race for 37 laps but finished 10th.
"Now it's all about the race and we want to close the deal," Carpenter said.
Hinchcliffe, who eight days ago suffered a concussion in the Grand Prix of Indianapolis and was cleared to drive on Thursday, averaged 230.839 mph.
"We got a little bit loose going into Turn Three on that last lap and had to crack the throttle and that’s what killed that final lap," said Hinchcliffe, who was also second in qualifying last year.
Power had an average of 230.697 to start on the outside of row one.
Three-times Indy 500 champion Helio Castroneves of Brazil will start fourth with Frenchman Simon Pagenaud and American Marco Andretti joining him on the second row.
Colombian Carlos Munoz and Americans Josef Newgarden and J.R. Hilderbrand make up the third row.
Colombia's Juan Pablo Montoya had the fastest average among drivers ineligible for the pole and will start 10th after averaging 231.007.
IndyCar Series champion and 2008 IndyCar winner Scott Dixon of New Zealand and former NASCAR champion Kurt Busch follow.
Busch will attempt to complete both the Indianapolis 500 and NASCAR's 600 mile race in Concord, North Carolina the same day.
(Reporting by Gene Cherry in Raleigh, North Carolina, editing by Ed Osmond)
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