Dixon, the 2008 Indy 500 winner, was joined on the front row for the May 28 race by Ed Carpenter and last year's champion Alexander Rossi.
"It feels damn good," the 36-year-old Dixon said after he posted an average speed of 232.164 miles per hour (373.632 kph) during his four laps.
"This is job one. Obviously the real deal is coming up in a week's time. That's when we're going to push even harder and capitalise more."
Alonso was competitive in the race, posting a 231.300 mph average speed that briefly put him in the lead.
"This is the biggest race in the world," he said. "I'm looking forward to next Sunday."
He said he was feeling more comfortable in the cockpit of an IndyCar and said participation in the race by European Formula One drivers like himself and Rossi was good for motorsports.
"I don't think that we need to separate too much F1 or IndyCar or rally or stock car. I mean, at the end of the day, it's just motorsports."
Wind and track temperatures that reached 114 degrees Fahrenheit (45.6C) made for challenging racing conditions, which caused Japan's Takuma Sato to brush up against the wall twice during his run.
The 40-year-old still posted an average speed of 231.365 mph, good for fourth.
Hot weather is expected again next weekend when over 300,000 fans will descend on the Speedway for the "The Greatest Spectacle in Racing" on the sprawling 2.5 mile (4.02 km) oval speedway.
France's Sebastien Bourdais, who sustained multiple hip fractures when he crashed during qualifying on Saturday, underwent surgery Saturday night and is recovering, according to a statement.
"I want to thank everybody for the support and the messages, quite a few drivers have already dropped by," he said.
"It's going to take time, but I'm feeling pretty good since the surgery. I'll be back at some point. Just don't know when yet!"
(Reporting by Rory Carroll in San Francisco, Editing by Gene Cherry/Greg Stutchbury)
