Leicestershire-based Rutter had claimed his third pole position of the season seconds before the rain came down.
Stoner, who has announced he will retire at the end of this season, claimed his third pole position of 2012.
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"I will try to do my best to win the race, which is the most important thing, " said Massa, who claimed his third successive pole in Sao Paulo.
Justin Wilson, who started 24th because he never got a qualifying run in on Saturday, drove all the way to third and pole-sitter Dario Franchitti was fourth in his 250th career start.
Felipe Massa, who is the worst-placed of the four drivers in the title fight, starts from his third consecutive pole position after snatching top spot from local hero Fernando Alonso by just 0.03 seconds in the dying moments of qualifying on Saturday.
Hamilton, who was third in China after starting from pole, and fifth in Bahrain, paid tribute to the team's efforts to improve the cars.
Just as Bahrain suits Massa, so does Turkey and the Brazilian forced his way back into the title race by turning pole position into his third straight win in Istanbul.
Mercedes then bought the team, based in Oxfordshire, England, in 2010 and it is once again on an upward curve, taking three pole positions and two third-places on the podium so far in 2013.
Pole sitter Brad Keselowski finished third, with hometown driver Kyle Busch in fourth and Carl Edwards fifth.
It was Junquiera's second pole of the season and third of his career.
With team-mate Felipe Massa qualifying third, half a second behind Alonso and pole-sitter Sebastian Vettel, and ahead of the German's Red Bull team-mate Mark Webber, it was Ferrari's best qualifying result of the season so far.
Stoner won that event in Jerez, having started fifth on the grid, but finished third in the season opener in Qatar despite claiming pole position.
Alonso took the lead for good with 13 laps to go and won by 10 seconds from Lotus' Kimi Raikkonen, with pole sitter Lewis Hamilton of Mercedes finishing third, just two-tenths of a second ahead of Red Bull's Sebastian Vettel.
Fernando Alonso produced a stunning lap to grab pole, while team-mate Felipe Massa qualified third fastest behind 2009 champion Jenson Button's McLaren.
Lorenzo, who also took pole at the Jerez Frontera circuit last year before finishing third, leads the overall standings with 41 points.
Pole sitter and three-time reigning world champion Vettel was third in a Red Bull.
Massa had taken a surprise pole ahead of Raikkonen but Hamilton leapt off the line from third to chase Massa.
Hamilton, who has started on pole for the opening two races of the season, finishing third each time, will now occupy the third row at best due to the penalty.
With Glock passing pole-sitter Trulli off the line for the lead, Hamilton rocketed into third, with Button also slipping ahead of Vettel.
Twelfth seed Agnieszka Radwanska enjoyed a relatively comfortable passage into the third round with a 6-3 6-4 win over Croatia's Petra Martic, and the Pole will play Simona Halep after the Romanian beat Russia's 24th seed Alisa Kleybanova 6-4 7-6 (7-2).
The 18-year-old from Oxford started from pole and held off the challenge of Spain's Nicolas Terol, with previous championship leader Julian Simon third.
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