Rubens Barrichello was 0.128 slower than Montoya in second place, while Schumacher was third with 1:20.784.
Valtteri Bottas won the battle but Lewis Hamilton won the war, securing his sixth Formula One world championship on Sunday, despite finishing second to his Mercedes team mate at the US Grand Prix.
Last season, the Ferrari driver left Magny-Cours after winning his fifth world title with six races to spare.
Red Bull's double World champion Max Verstappen won the Mexico City Grand Prix on Sunday to set a Formula One record of 14 victories from a single season, as well as the most points scored.
Belgian driver Jerome d'Ambrosio will race for Lotus in the Italian Formula One Grand Prix at Monza this weekend in place of the suspended Romain Grosjean, the team said on Tuesday.
Britain's Lewis Hamilton won a wet and sombre Japanese Grand Prix on Sunday to extend his Formula One lead over Mercedes team mate Nico Rosberg to 10 points with four races remaining.
Valtteri Bottas announced split from wife Emilia, an Olympic swimmer
Is Lewis Hamilton sufficiently appreciated at home?
Nico Rosberg cruised to victory in the first Formula One race held in Azerbaijan on Sunday and increased his championship lead over Mercedes team mate Lewis Hamilton to 24 points. While the German enjoyed an uneventful drive in the late afternoon sunshine, triple world champion Hamilton worked up a head of steam as he wrestled with his car's settings without the team being able to help.
The German's future remains uncertain even if he has said repeatedly that he expects to be in Formula One next season.
The 22-year-old Briton will line up alongside Ferrari's Kimi Raikkonen on the front row for Sunday's race.
Perez, who vaulted to fourth in the overall standings after Sunday's race, is the first Mexican driver to win a race since Pedro Rodriguez took victory in the 1970 Belgian Grand Prix.
Launching a scathing attack over his fellow drivers for not presenting a united front on the introduction of Halo device, Ferrari's Sebastian Vettel has favoured the launch of head protection device for the 2017 Formula One season saying nothing could 'justify death'.
The feeling in the paddock is that the FIA's World Motor Sport Council could hit them with at least a heavy fine and points penalty.
Narain Karthikeyan finished 17th in the first qualifying round at the San Marino Grand Prix
Lewis Hamilton has had more success in Shanghai than any other Formula One driver, which makes Sunday's Chinese Grand Prix the ideal location for the triple world champion to end Mercedes teammate Nico Rosberg's winning streak. While Rosberg has started the season with a perfect 50 points from two races, and a run of five successive victories dating back to last November, Hamilton is ready to turn the tables. The Briton has won four times in Shanghai and is on for three in a row after last season becoming the only driver to win the race in successive years. "It's not been a smooth start to the season for me, so to be in the championship position I'm in right now is actually pretty positive," said Hamilton, who lies second in the standings after a second and a third place. "Now we go to China for the next battle. It's a track that's been good to me over the years... so hopefully this race can be the turning point." Hamilton has not won since he took his third world championship in Austin, Texas, last October but the 31-year-old has started both races this season on pole position.
Australian Mark Webber seized pole position for the South Korean Formula One Grand Prix on Saturday with title-chasing Red Bull teammate Sebastian Vettel having to settle for second place on the starting grid.
Thunder, lightning and torrential rain washed out second practice at the U.S. Formula One Grand Prix on Friday after Nico Rosberg went fastest for Mercedes in a largely meaningless morning session.
Red Bull's Mexican Sergio Perez was a distant third, struggling with dehydration after a water bottle failure in the Texas heat.
Five-times Formula One world champion Lewis Hamilton led a Mercedes front-row lockout with a blistering pole position at the season-ending Abu Dhabi Grand Prix on Saturday.
Formula One carmakers are prepared to set up their own championship without Ferrari if need be, said Renault team president Patrick Faure.
Lewis Hamilton stormed to pole position at the Brazilian Grand Prix on Saturday with Mercedes team mate and title rival Nico Rosberg joining the triple Formula One world champion on the front row. On a damp and overcast Sao Paulo afternoon, it was the 60th pole of the Briton's career, eight short of Michael Schumacher's record, and his first in Brazil since 2012 when he was at McLaren. With his title on the line, it was also one of Hamilton's most important in a roller-coaster season marked by mechanical setbacks.
Formula One is as safe as it has ever been but danger will always be part of the sport.
The Nuerburgring circuit will not host the German Formula One Grand Prix this year, an official for the company said on Thursday after Hockenheim also ruled out the possibility.
Ferrari's world champion Kimi Raikkonen will lead the way when Formula One returns to Barcelona this weekend for the first race of the season in Europe. The Finn is top of the standings after the first three long-haul races, a novel sensation for a driver who won his title by clawing back a 17-point deficit in the last two rounds of 2007.
Germany's Nico Rosberg took Mercedes' second successive pole position in qualifying for the Bahrain Formula One Grand Prix on Saturday.
Germany's Nico Hulkenberg will replace Racing Point driver Sergio Perez at this weekend's British Formula One Grand Prix after the Mexican was ruled out by a positive COVID-19 test result. Hulkenberg, a veteran of 177 Grands Prix, raced for the team when they were known as Force India. He competed for Renault last season.
Ferrari's Fernando Alonso won the European Grand Prix on Sunday to become the first repeat winner of the Formula One season after eight races.
The win also set a record, one that Hamilton had previously shared with seven times champion Michael Schumacher, of 41 wins from pole position.
World champion Sebastian Vettel won the Korean Grand Prix in a Red Bull one-two finish on Sunday to take the overall Formula One lead from Ferrari's Fernando Alonso with four races remaining.
Bookmakers William Hill have the Briton as 15/8 favourite for the 2018 drivers championship, with Ferrari's Sebastian Vettel at 3/1 and Red Bull's Max Verstappen at 10/3.
Kimi Raikkonen gave Lotus a dream start to the Formula One season on Sunday with a winning strategy carried out to perfection in the Australian Grand Prix.
Lewis Hamilton boosted his morale with the fastest lap in Russian Grand Prix practice on Friday after Mercedes team mate Nico Rosberg set the early pace and Ferrari suffered reliability problems.
Lewis Hamilton's hopes of clinching his fifth Formula One World championship at the US Grand Prix were boosted on Friday when Ferrari rival Sebastian Vettel was handed a three-place grid penalty for a practice infringement.
"I just love fighting on the circuit and it's natural to me and as long as I am competitive and the love is there," said the 35-year-old German.