Alonso's display arrived after a disastrous start to the weekend which began with a spectacular Honda engine failure in Friday's opening practice.
The engine problem was the latest in a series of power unit issues the Spaniard has suffered in what has been a woeful campaign for the Woking squad.
Boosted by his showing, Alonso, who is set to contest the Indianapolis 500 later this month, is hoping to convert his grid spot into championship points.
“Maybe on the oval I learned how to go quick on the straights as well,” Alonso joked, following his Indianapolis 500 test earlier this week.
“It was a good qualifying for us and P7 is a gift, so we'll see what we can do tomorrow (Sunday).
“As I said yesterday, sometimes the weekends start the wrong way but then they fix themselves, and vice versa. The important thing is tomorrow, to try to get a few points.
“Yesterday was not a normal session.
“We had the problem in the first session and then in the second the car was half ready. But I said we would be a bit more competitive today.
“It was better than expected but the support from the people gives you a few extra tenths.”
Alonso's team-mate Stoffel Vandoorne struggled for pace and will start Sunday's race from 19th on the grid.