Kovalainen, 26, won from Toyota's Timo Glock with Ferrari's Kimi Raikkonen in third place.
He was also delighted with Kovalainen's progress, saying he out paced Hamilton in Malaysia.
Lotus are expected they will continue with Jarno Trulli and Heikki Kovalainen as drivers in 2011.
Afterwards, Kovalainen revealed he "didn't have the grip and...no confidence to push it (the car) whatsoever".
Finn Kovalainen is also out of contract and under pressure at McLaren after failing to realise his early potential.
Heikki Kovalainen in the second McLaren overhauled Kimi Raikkonen's Ferrari to take third place on the grid.
Massa charged off the start to overtake polesitter Hamilton and Kovalainen, who had occupied the front row.
The 21-year-old GP2 champion was third fastest behind Renault's Nelson Piquet Jr and Heikki Kovalainen on Thursday.
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Toro Rosso's Sebastian Vettel took the final points place, holding off Heikki Kovalainen's McLaren in the closing laps.
But despite putting together some decent laps he had to settle for fourth on the grid behind Kovalainen.
Rookie Heikki Kovalainen was the faster of the two Renaults in seventh place, just ahead of Giancarlo Fisichella.
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Pre-season favourite Heikki Kovalainen saw his title hopes disappear when he could only finish third in race one.
McLaren team-mate Kovalainen, who finished fifth in Hungary, is also expecting to capitalise on the cars' improved performance.
Button moved up from ninth to fifth and then into second in the closing stages before Kovalainen's late show.
He managed some running in the afternoon and ended up ninth fastest, behind the impressive Lotus of Heikki Kovalainen.
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Nico Rosberg, who was fastest in final practice, claimed fifth spot ahead of Ferrari's Felipe Massa and McLaren's Heikki Kovalainen.
The Englishman and team-mate Heikki Kovalainen took the wraps off the new Mercedes-powered MP4-24 at the team's base in Surrey.
Renault rookie Heikki Kovalainen has made the top 10 and outqualified team-mate Giancarlo Fisichella for the second time this season.
Heidfeld held a watching brief in the early laps and stayed out of trouble to benefit from Kovalainen's late problem.
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Ferrari's Massa finished third in second practice, while Heikki Kovalainen of McLaren and Williams' Nico Rosberg took fourth and fifth, respectively.
Malaysian Fairuz Fauzy will take part in first practice in Hockenheim for Lotus in place of either Jarno Trulli or Heikki Kovalainen.
McLaren's world champion left it late with a lap 0.047 seconds faster than team-mate Heikki Kovalainen, who had topped the morning timesheets.
Behind Sebastien Bourdais in his Toro Rosso, Kovalainen will start 18th, his lowest grid slot since joining McLaren prior to last season.
Kovalainen revealed later that he had accidentally hit the pit lane speed limiter button while removing an oil-smeared tear-off from his visor.
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Red Bull's Mark Webber recorded the fastest time -- 1m21.953 -- followed nearly two seconds back by Hamilton's team-mate, Heikki Kovalainen.
Ferrari endured a bad day with Kimi Raikkonen down in 18th place, one behind compatriot Heikki Kovalainen of McLaren, and Giancarlo Fisichella 20th.
"Welcome to my world, " said Hamilton, whose team-mate Heikki Kovalainen made it through qualifying session one and will start Sunday's race a row in 14th.
World champion Lewis Hamilton will start from 18th place, one behind McLaren teammate Heikki Kovalainen, as both failed to make it past the first hurdle.
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Kovalainen drove alongside Lewis Hamilton for McLaren in 2008 and 2009, but his place this year has been taken by reigning world champion Jenson Button.
Hamilton knew he could beat his former team-mate Heikki Kovalainen day in day out, and so all the resources and effort were focused on him.
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