The 35-year-old won the qualifier after his lap in one minute and nine seconds.
Grosjean is in his first Indycar season, the win in the qualifiers is his first in just three starts.
- When I saw the qualifying group, I thought that, if we manage from the first group, we will be okay, which we did.
We were really on it during the last laps, what a day it was for us, says Grosjean.
He will start in pole position later tonight when the competition starts.
- I am happier than I have been for a very long time, he says.
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The Frenchman has previously driven Formula 1 for ten seasons.
However, his F1 career ended last November when he was involved in a violent crash during the Bahrain GP.
Grosjean suffered severe burns to his hands after his car split in two and started to burn.
After the qualifying win, he is hailed by, among others, the former F1 world champion Jenson Button and Marcus Ericsson.
"Fantastic news!", Button writes on Instagram.
"Congratulations, very impressive," comments Ericsson.
Swedes Felix Rosenqvist and Marcus Ericsson finished in 13th and 15th place respectively.
ARCHIVE: Here the F1 driver cheats death - see the dramatic pictures (29 November 2020)
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Formula 1 driver Romain Grosjean escapes from the burning car.
Photo: Viaplay