The German overcame a mid-race drop in pace to keep world champion Alonso at bay in front of Ferrari's home fans and celebrated by insisting he is now a serious title contender.
Schumacher ended a four-race winning streak for Renault with his first genuine win since 2004 but he denied today's performance was a one-off at a track well suited to his Bridgestone tyres.
Schumacher, who has jumped to second in the championship, 15 points behind Alonso, said: "It feels great - what else can you say? We had an amazing weekend.
"The championship had not really gone away with two difficult races but points-wise it is looking better.
Whoever maximises their performance will be in front."
Schumacher had to fend off a charging Alonso for the second half of the race in a repeat of last season's nerve-jangling climax, but with the roles reversed.
As happened last year, there was no way past for the faster car but Schumacher confessed he had to draw on all his experience to keep Alonso back.
Alonso, who celebrated his world championship last year with an improbable overtaking move on Schumacher at Suzuka, admitted that even he ran out of ideas.
The 24-year-old was content to settle for second, safe in the knowledge that his championship lead has again been stretched. He eased off in the final few laps after almost throwing his eight points away when he ran wide four laps from the end and added: "This eight points is perfect for me.
"The second in the championship were Kimi Raikkonen and Giancarlo Fisichella and they took only a few points, for fifth and eighth respectively.
"Championship-wise it is the perfect result."
McLaren's Juan Pablo Montoya stood on the podium for the first time this season after taking advantage of Jenson Button's troubles to claim third.
Button had looked certain to take the final podium spot after a strong start, but he suffered a nightmare pit stop which ruined his chances.