The Spaniard lost pole position to McLaren's Jenson Button at the first corner but retook the lead after the pit stops to hold on for a 2.9-second victory.
Felipe Massa of Ferrari was third and Red Bull's Sebastian Vettel came fourth.
Red Bull driver Mark Webber, who finished sixth, leads the overall standings with 187 points. Lewis Hamilton crashed out on the first lap and is second with 182. Third-place Alonso has 166, Button 165 and Vettel 163.
Alonso said his 24th career victory came second only in importance to his Spanish GP win in 2006 as it gave him hope of a third world title with five races left.
"We made the right choices in the right moments," Alonso said after his third victory of the season. "With the result we gain some confidence and motivation for the whole team not to give up. (But) we need to remain calm. We need to find some consistency, that would be the key." Alonso was making his debut at Monza for the Italian team and it was Ferrari's first victory at its home track since Michael Schumacher won in 2006.
Alonso was already celebrating his win in front of fans ahead of the finish line after tying Juan Manuel Fangio of Argentina for eighth all-time. A huge heart-shaped Ferrari banner was unhurled in front of the podium before the champagne came out.
"I never imagined that it was so good," said Alonso, who won here for McLaren in 2007. "A very emotional week." Button made a great start to move ahead of Alonso, who struggled to hold off teammate Massa only days after the pair were cleared over a team orders controversy in a 1-2 finish at the German GP on July 25.
"It was all looking very good but it was a tough race mentally to have Fernando behind you," defending world champion Button said. "I spent the whole time looking in my mirrors trying to judge how far Fernando was behind." Webber started poorly for the second straight race but Hamilton fared even worse. He exited before the halfway point of his first lap after bumping with Massa as the pair jostled for third with the McLaren driver's front right wheel damaged.
"I only have myself to blame," Hamilton said. "I tried my best and some things just don't go your way." Webber easily passed Vettel on the 21st lap to sit seventh even though his German teammate was lapping faster.
But Vettel, who had started sixth, eventually got past and worked his way up the field to recover from the Belgian GP, where he finished out of the points after crashing into Button.
Alonso was able to get back in front after the top two pitted, emerging with less than a second advantage at the start of the 38th lap. He held the lead to the end.
Button said he struggled on the new tires after his stop.
"Everything was going smoothly but then we pitted one lap early and maybe that was a mistake," Button said. "That's for me where I lost time." Vettel confirmed his spot at the close as he pitted to make the mandatory tire change on his last lap. He returned in front of Nico Rosberg, who finished fifth for Mercedes.
Webber was left frustrated by a running duel with Nico Hulkenberg of Williams, who cut across chicanes several times as he battled with the Australian driver. Hulkenberg ultimately finished seventh.
"We underperformed as a team today," Webber said. "We could have capitalized and got more points, but we sniffed around just getting a few. It's a bit disappointing but at least we got some (points)." Spanish team HRT said a member of its team "had an incident" during driver Sakon Yamamoto's pit-stop. An ambulance arrived in the pit lane to attend to the person.
No further details were immediately available.
F1 now departs Europe to begin a three-race swing through Asia, starting with the Singapore GP night race on Sept.
26.
