Hinchcliffe, from Oakville, Ont., qualified in the No. 2 position for Andretti Autosport after missing the pole by a miniscule 0.0023 seconds.
Tagliani, from Lachenaie, Que., had pole position last year and will start 11th this year for Team Barracuda-Bryan Herta Autosports.
Both men are looking for better races than last year.
Hinchcliffe, who only joined Andretti in January after being named rookie of the year for 2011, joked that last year he ran the Indy 250. He tagged the wall midway through the 200-lap race.
But driving the car Danica Patrick made famous has injected a lot more success into his sophomore season, although the 25-year-old said questions remain about the car since it was rebuilt.
"It's the first time anybody will have run this car for a full race on an oval," he said in a conference call Wednesday.
"With the heat we're expecting Sunday, I think that throws a question mark in the mix."
The car has been renumbered No. 27, the same number that adorned the car Jacques Villeneuve drove in 1995 when he became the first and only Canadian ever to win at Indianapolis.
In a twist of fate the number had been intended for Dan Wheldon, last year's Indy 500 winner who was killed last Oct. 16 at the IZOD IndyCar World Championship at Las Vegas Motor Speedway.
And Tagliani, Wheldon's teammate last year at Indy, said his car is adorned with the same No. 98 that adorned Wheldon's car last year — part tribute, part superstition perhaps.
"I don't know why but I'm definitely looking at No. 98 as a number that brought a lot of luck to the team and also did a lot at the speedway," said the 39-year-old.
He finished only one position ahead of Hinchcliffe in 2011, after making contact with the wall a little more than 50 laps from the end of the race.
But high engine oil temperature issues with his Lotus engine had already moved him well back in the pack. He's looking for something better this year from the Honda engine he'll be running.
"We have a good car in traffic at the moment. We did a lot of race trim running and it's been really, really good. I'm very excited. I've never been so confident before a race in my life."
Tagliani ran into trouble on the same turn four that cost race leader J.R. Hildebrand the title last year at Indy, when he also ran high and clipped the wall on his final lap. That opened the door for Wheldon.
This is Tagliani's fourth visit to Indy. His best finish was a 10th in 2009 and he said it's always a tough race to predict with eight or nine pit stops and so many things that can happen.
The chassis this year is still an Italian Dallara but this season engines have been downsized from 3.5 litres to 2.2 litres and they've been supercharged. To make it more interesting, the forecast for Sunday is in the mid-to-high 30s.
"Setups are going to be a shot in the dark," said Hinchcliffe.
"It's going to be about compromise and adaptation I think."
His Chevy engine may give him an edge in fuel consumption, which is a big part of winning the Indy 500, but he isn't counting on it too much. Chevrolet-powered cars have also won the first four races of the season.
"Racing's not about engines or tires or race cars, it's about people and the right group of people will be successful, period," said Hinchcliffe.
Engines do seem to help this season. The top six finishers in the qualifying round at Indianapolis were all powered by Chevrolet. Josef Newgarden, at No. 7, and Tagliani were the top drivers for Honda.
"We have to forget about the first three races or four (of this season)," said Tagliani, adding that the same holds true for qualifying times.
"Racing's 10 times harder than qualifying. Hopefully there's somebody up there that has worn the 98 in the past who can keep an eye on us and give us some luck and we'll be all right."