After an inconsistent start, he gradually got the better of the much more experienced Ralf Schumacher.
Coulthard's team-mate Kimi Raikkonen finished third, beating Montoya's team-mate Ralf Schumacher into fourth place.
Ralf Schumacher scythed through the ranks from last to fourth, outmanoeuvring and overtaking his brother on the way.
Then Ralf Schumacher gave me a puncture, I got a pit lane speed penalty and then I spun.
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Cerraron el marcador Giancarlo Fisichella (Renault), Ralf Schumacher (Toyota) y Jacques Villeneuve (Sauber).
Juan Pablo Montoya and Ralf Schumacher claimed the third and fourth places, respectively.
Montoya then got embroiled in a controversy with team-mate Ralf Schumacher, who tried to overtake him on the hill after Tosa.
BBC: SPORT | Motorsport | Formula One | Montoya slams Schumacher
"We had a one-two last week and again today and hopefully the two of us can keep going, " said Ralf Schumacher.
The Williams pair of Juan Pablo Montoya and Ralf Schumacher bounced back from their disqualification in Canada to finish fifth and sixth.
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"Juan Pablo's second place in Malaysia has shown that we're not as far away from Ferrari as we feared, " said Ralf Schumacher.
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With Ralf Schumacher following his brother Michael into retirement, Jarno Trulli assumes the lead driver position in his fourth season at Toyota.
With Ralf Schumacher's clash with the same driver so fresh in the memory, particularly after the protracted legal battle, Williams shared his frustration.
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The new Fuji track was inaugurated on Monday by Toyota F1 driver Ralf Schumacher, who competed there in Formula 3000 in the mid-1990s.
The more experienced and consistent Ralf Schumacher will be disappointed if his Williams doesn't figure at the front end of the grid and the race.
Ralf Schumacher is now 11 points behind his brother in the title chase, with Kimi Raikkonen in second six points adrift of the Ferrari star.
His right rear tyre then suffered a puncture after a light touch from Ralf Schumacher's front wing as the German passed him on lap five.
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Juan Pablo Montoya is set to leave Williams for McLaren at the end of the season, while Ralf Schumacher could be on his way out too.
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The Renault passed both Trulli and Rubens Barrichello's Ferrari with some strong driving around his stop, and then passed Ralf Schumacher in a controversial move on lap 50.
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Michelin had advised its seven teams not to race without changes because of the tyre failure that lead Ralf Schumacher to smash into a wall in Friday practice.
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Toyota's Ralf Schumacher is surprisingly one of the drivers eliminated.
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Williams' only success came through Ralf Schumacher in Malaysia.
The safe option might be Pizzonia, but he was no more than adequate when he filled in for the injured Ralf Schumacher last season - and the team's competitiveness noticeably improved when Schumacher returned.
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And on Friday, former F1 driver Ralf Schumacher told German newspaper Bild that he had been in talks with the team about an F1 comeback, saying Stefanovich made "a very serious and purposeful impression".
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"After a busy start to the Formula One season with four flyaway races in succession, it will be nice to come back to Germany, " said Schumacher, whose younger brother Ralf -- a former F1 competitor -- drives in the DTM series.
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