The win, with Ferrari's [ Images ] Michael Schumacher [ Images ] starting in the pit lane after being stripped of pole for deliberately obstructing rivals in qualifying, stretched the Spaniard's overall lead to 21 points.
It was the 12th win of the 24-year-old's career, his first in Monaco and fourth of the season. He has 64 points to Schumacher's 43, with the German fighting back from last place to fifth.
Colombian Juan Pablo Montoya [ Images ], the 2003 winner for Williams, finished second in his McLaren [ Images ] team's 40th anniversary race with Briton David Coulthard [ Images ] taking Ferrari-powered Red Bull's first podium finish in third place.
It was the two times Monaco winner's first top three finish since Japan [ Images ] 2003 with McLaren.
The Scot's joy was Italian Jarno Trulli's [ Images ] despair, with the Toyota [ Images ] driver in third place and heading for his first points of the season until he pulled over with five laps remaining.
Honda's Brazilian Rubens Barrichello [ Images ] was also left regretting what might have been after collecting a drive-through penalty 15 laps from the end while running third. He finished fourth.
Brazilian Felipe Massa [ Images ] was ninth for Ferrari after starting on the back row in a qualifying nightmare for the team.
The pressure was off Alonso after McLaren's Kimi Raikkonen [ Images ], last year's winner on the streets of the Mediterranean principality, pulled over with a smoking engine on lap 51. The team suspected a burning heat shield was to blame.
Until then the Finn had taken the fight to the Spaniard, pushing him from the second lap and the two running nose to tail and rarely more than a second apart as they carved round the treacherous street circuit.
An over-zealous marshal then sprayed the car with foam while Raikkonen was still sitting in it, adding to his general discomfort. The Finn walked off unhappily to watch the rest of the race from a yacht in the harbour.
Alonso, inheriting pole position after Schumacher's punishment, made a clean start with Australian Mark Webber [ Images ] holding on to second place for Williams through the first corner with the two McLarens close behind.
Raikkonen then forced his way past Webber on the second lap on the hill going up to Casino Square and the battle was on between last season's two protagonists with the Finn constantly in Alonso's mirrors.
With Barrichello acting as a stopper in fifth place, the leaders pulled away and the top three were unchanged, with Webber leading for a lap at the first pitstops, until the 49th lap when the Australian's engine expired.
A marshal extinguished the flames licking the engine covers, as the disgusted Australian stalked off with his dreams of a podium shattered.
"I'm were very, very disappointed, I thought we were on (the podium), I felt we deserved something today... We were on qualifying pace for an hour," Weber told ITV Sport.
The incident brought out the safety car for the first time and Alonso and Raikkonen seized the chance to pit immediately. It was still out when Raikkonen pulled over.