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With the championship poised ever more on a knife-edge, the top three contenders were separated by two points, with Ferrari's Schumacher on 72, Williams's Juan Pablo Montoya on 71 and McLaren's Kimi Raikkonen on 70.
None of that concerned Alonso, the 22-year-old Spaniard dominating the race from pole position on Sunday to take the chequered flag with a comfortable 16.7 second advantage over runner-up Raikkonen.
He was the first Spaniard to win a grand prix.
Colombian Montoya was third, despite a late spin, while five-times world champion Schumacher trailed home eighth to salvage just one point at the circuit where he celebrated his fourth title in 2001.
Ralf Schumacher was fourth for Williams, fighting back impressively and overtaking more cars than anyone else after a first-lap spin sent him from the front row to 18th place, with McLaren's David Coulthard fifth.
Australian Mark Webber, running second for the first 12 laps with his slower car acting as a bottleneck as Alonso sped into the distance, took sixth place for Jaguar.
Italian Jarno Trulli was seventh for Renault. Michelin tyres were used by all the top seven cars.
RECORD BOOKS
Alonso, 22 on July 29, replaced American Troy Ruttman in the record books as the youngest race winner. Ruttman won the 1952 Indianapolis 500 aged 22 and 80 days when that event counted towards the championship.
New Zealander Bruce McLaren was until Sunday the youngest grand prix winner, taking the U.S. Grand Prix at Sebring in 1959 in a Cooper Climax at the age of 22 years and 104 days.
Alonso was Renault's first winner as a constructor for 20 years, the last being French champion Alain Prost in Austria in 1983, and the eighth different winner from five teams in 13 starts this year.
In the constructors' championship, Williams rubbed salt in Ferrari's wounds by taking the overall lead from the champions with 129 points to the Italian team's 121.
Ferrari's hopes of staying ahead had already been dealt a blow by the departure of Brazilian Rubens Barrichello, who crashed heavily on lap 21.
Barrichello, winner at the Hungaroring last year when Ferrari clinched their fourth successive title, plunged straight ahead into the tyre wall at the end of the main straight after what appeared to be a disastrous suspension failure.
The Brazilian walked away unhurt.
Zsolt Baumgartner, replacing injured Briton Ralph Firman at Jordan as Hungary's first Formula One driver, lasted 35 laps before he pulled over with a blown engine.
He could at least console himself with the thought that he ran for longer than Italian team mate Giancarlo Fisichella, the third retirement of the race.
