The qualifying session stayed dry but rain could still affect the outcome of the race.
But British hope Jenson Button starts from back in 17th after another disappointing qualifying session.
Rosberg squeezed into the final qualifying session in 10th but could barely improve with ninth place.
McLaren will analyse the data before making a decision on whether to run the F-duct for Saturday's qualifying session.
The two title rivals recommenced battle in a closely-fought qualifying session at Interlagos.
For the second GP running he did not emerge from qualifying session one - and will start 16th for Sunday's race.
It was a happier qualifying session for Webber's compatriot, Daniel Ricciardo who steered his Toro Rosso to a highly creditable seventh.
The reports surfaced last Saturday after a qualifying session in which Alonso had blocked Hamilton's exit from the pits in Budapest.
The strange qualifying session was compounded by the fact that in the closing minutes all the official timing screens went down.
But after a promising qualifying session on Saturday, where he secured fifth place on the starting grid, he eventually finished eighth.
That Kubica ended fastest confirms the Renault driver could have a major say in what promises to be a furiously hard-fought qualifying session.
The qualifying session saw Spain's Lorenzo briefly threatened to spoil Stoner's party when he recorded the fastest lap with fewer than 15 minutes remaining.
The two Toro Rossos of Sebastien Bourdais, who shocked the field by leading the first qualifying session, and Sebastian Vettel rounded out the top ten.
"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.
He will hope to make up much more than that after getting the better of a qualifying session disrupted by heavy downpours in Sao Paulo.
Massa, who was nearly half a second slower than Alonso, said it was a good team performance in what he described as a "tough" qualifying session.
The 41-year-old, back in the sport after three years in retirement, also had his worst qualifying session of the campaign and started 13th on the grid.
It was also a disappointing qualifying session for Williams, although Kazuki Nakajima will be pleased to out-qualify team-mate Nico Rosberg for the first time this season.
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But it was Massa who twice set the benchmark in the final qualifying session and Hamilton could not eke out enough pace to eclipse the Brazilian.
But the Australian, fastest in the wet during Friday's opening qualifying session, could not sustain his speed and finished in third, splitting the McLarens of Coulthard and Raikkonen.
Germany's Nick Heidfeld, still seeking to clinch a new contract with BMW Sauber, was the biggest casualty of the first qualifying session as he could finish only 16th.
Championship leader Jenson Button bounced back after a disappointing qualifying session to finish fifth, ahead of his teammate and rival for the title Rubens Barrichello who finished sixth.
Mercedes drivers Michael Schumacher and Nico Rosberg also endured a less than satisfactory qualifying session, with Rosberg qualifying in 13th and Schumacher, a seven-time world champion, only managing 17th.
Vettel had hoped his achievement in securing pole position in Saturday's rescheduled qualifying session would help his quest for a fourth successive title get off to the perfect start.
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The only positive to come out of Button's day was that Vettel, his only other challenger for the title, could not even make it out of the first qualifying session.
Which meant that Alonso had his work cut out for him after a mediocre qualifying session put him ninth on the grid for the race with Vettel in pole position.
In double world champion Fernando Alonso's final appearance for Renault before he leaves for Ferrari, the Spaniard suffered the worst qualifying session of his underwhelming season to finish down in 16th.
"It wasn't easy with the traffic, people going off and the yellow flags but we went through to the second qualifying session tomorrow so it's not all bad, " said 2007 world champion Raikkonen.
The first qualifying session was stopped early on when Force India's Vitantonio Liuzzi smashed into the wall at Turn 17, losing control after running wide on the last corner and touching the artificial grass.
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