The 26-year-old German, who crashed out of the season's first race in Australia, started fourth but inherited the lead as others dropped out.
With temperatures reaching over 100 degrees and 97 percent humidity, Schumacher claimed his fourth career race Sunday, completing the 56-lap event in one hour, 34 minutes, 12.912 seconds. He averaged 122.561 miles per hour (197.680 kph) over 189.42 miles in his Williams-BMW.
A four-time champion and winner of the series title the last two years, Michael Schumacher started from the pole with Montoya second. The 33-year-old German cut across to stop Montoya from getting past, but the Colombian refused to yield and made contact with the Ferrari. Schumacher's front wing came off and he dropped down to 11th place after coming into the pit for a replacement.
Montoya also lost position but fought back to fourth place, only to be penalized by the stewards for the opening-lap incident. The Colombian is second to Michael Schumacher in the World Drivers' standings, 22-14.
After storming back to reach the leaders, Michael Schumacher took third place by overtaking Britain's Jenson Button in a Renault with half a lap left.
Ferrari's No. 2 driver, Rubens Barrichello of Brazil, started from the third spot and was running second when he suffered engine failure. He has not finished a race this season.
The McLaren-Mercedes team qualified on the third row, but endured a discouraging race. With both cars suffering engine failure, Scotland's David Coulthard retired on the end of lap 15 while Kimi Raikkonen's race came to an end on lap 24 as the Finn was in second place.