Ferrari's Felipe Massa finished sixth, a big relief for the under-pressure Brazilian who had scored just two points from the first five races.
Britain's Paul Di Resta and Force India team mate Nico Hulkenberg were seventh and eighth respectively with Kimi Raikkonen ninth for Lotus and Bruno Senna taking the final point for Williams.
In the constructors' standings, Red Bull have 146 points to McLaren's 108.
Frenchman Romain Grosjean was the big loser at the start, lining up in fourth place for Lotus but crashing out at the first corner with a broken suspension after tangling with the Mercedes of Michael Schumacher.
That incident brought out the safety car for two laps.
Schumacher, who had set the fastest time in Saturday's qualifying but was denied a first pole since 2006 due to a five place grid penalty carried over from Spain, retired in the pits after 64 laps.
Venezuelan Pastor Maldonado, heroic winner of the previous race in Spain, also crashed out on the opening lap after starting in last place for Williams thanks to two separate penalties.
In Image: Red Bull driver Mark Webber, of Australia, steers his car on his way to win the Monaco Formula One Grand Prix