Championship leader Nabil Jeffri will share the front row with Hare, who recorded a best lap time of 1:59.369 in lap 10. Jeffri finished 0.461 seconds behind.
34 points separate Hare and Jeffri with last four races left in the season.
Aditya Patel set a time of 2:00.656 to be sixth fastest.
"I am pretty much okay with the results but I am still six tenths off Aston