German Nico Rosberg finished eighth for Williams ahead of Force India's Adrian Sutil and outgoing champion Lewis Hamilton, who was 10th for McLaren Mercedes.
Kovalainen only narrowly finished ahead of the Force India duo, with neither Adrian Sutil nor Giancarlo Fisichella making it into Q2 for the 23rd consecutive race as they will start 19th and 20th.
The visitors began and finished the dominant side, with a smart handling move involving class act Adrian Vowles and Michael Eagar unlocking the Wildcats' defence for winger Darren Rogers to cross for a seventh-minute try.