Carpenter, who has clinched pole twice previously, and Alonso will join seven others in an nine-car shootout on Sunday to battle for pole to the May 28 race.
French hopeful Sebastien Bourdais suffered leg fractures in a crash and was scheduled to have surgery later on Saturday, officials said.
Despite rain that delayed qualifying for five hours, Alonso said he was pleased with his performance.
"I think the day was smooth for us," the Spaniard told reporters.
"I think this morning when the weather came in, (it) definitely put a little bit of a stress on everyone. Obviously you have only one attempt, one shot, so you cannot get it wrong."
"I think (it) was not perfectly OK in terms of balance, in terms of driving myself, that I keep learning on this format.
"Useful run today, useful lessons. So tomorrow I will try to do better and find more speed."
Carpenter topped Japan's Takuma Sato (230.382) and New Zealand's Scott Dixon (230.333) to lead qualifiers.
Carpenter was among the drivers who took to the track late in qualifying when the weather was cooler and it proved to be an advantage.
JR Hildebrand (230.205 mph), Alexander Rossi (230.148), Will Power (230.072), Tony Kanaan (230.007) and Marco Andretti (229.924) rounded out the top nine.
(Reporting by Gene Cherry in Raleigh, North Carolina; Editing by Greg Stutchbury)
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