Seven times world champion Michael Schumacher [ Images ], chasing his 85th win after taking a record-equalling pole position on an all-Ferrari front row, had to settle for second place after a thrilling battle with his young rival.
Alonso, the 24-year-old Spaniard who last year became Formula One's youngest champion, made sure of his ninth victory after emerging from his final pitstop just as the 37-year-old German was about to go past.
The two cars almost touched as they fought for the advantage, with Alonso holding firm to win by over a second and to start the season as he finished the last one, on top of the podium.
McLaren's [ Images ] Kimi Raikkonen [ Images ] finished third, a remarkable result for the Finn who had to carve through the field on a one-stop strategy after a suspension failure in Saturday's qualifying pitched him to the back of the grid.
Briton Jenson Button [ Images ], a pre-race favourite for Honda, finished fourth and is still seeking his first Grand Prix win after 101 starts.
Rookie Nico Rosberg [ Images ], son of 1982 world champion Keke, was seventh for Williams, becoming the 54th driver in the history of the sport to score on a race debut after overtaking Austrian Christian Klien's Red Bull on the last lap.
Schumacher, spearheading Ferrari's [ Images ] recovery from a dismal 2005 season, had led from the start while a determined Alonso roared past the German's new Brazilian team mate Felipe Massa [ Images ] at the third corner after starting fourth.
Massa's race was wrecked when he spun on lap eight, narrowly missing Alonso's Renault as he skidded sideways past the Spaniard, and then pitted.
There was confusion in the Ferrari pits as mechanics struggled to remove the rear right tyre with a faulty pneumatic wheel gun.
The Brazilian was kept waiting 46.8 seconds before rejoining the race among the tailenders. He finished ninth.
While he went from front to back, Raikkonen clawed his way back into contention. The Finn was up to 13th at the end of the first lap.
Renault's Giancarlo Fisichella [ Images ], winner of last year's Australian season-opener, slowed and retired on lap 22.
Canadian Jacques Villeneuve, the 1997 champion, hurriedly exited his BMW Sauber [ Images ] after the engine blew and then flared up in flames as he pulled over.
For the first time since 2002, when Toyota [ Images ] entered the sport, 22 cars and 11 teams lined up on the starting grid with the arrival of newcomers Super Aguri.
Formula One's newest team, with an uncompetitive car derived from a 2002 Arrows, showed they had plenty learn when rookie Yuji Ide was hit with an immediate drive-through penalty because his mechanics were late in leaving the grid.
Ide later overshot his mark on a pitstop and hit one of those mechanics.
The Midland team, making their debut after the name change from Jordan, fared little better with Dutchman Christijan Albers retiring at the start.