Stoner, who started on pole, defied terrible racing conditions on a drenched Silverstone circuit to clinch a fourth victory in six rounds, becoming the first Honda rider to win three successive MotoGP races since Italian great Valentino Rossi in 2003.
Lorenzo was in second place when he crashed out on the eighth of 20 laps, seconds after teammate Ben Spies also fell. The heavy rain then accounted for Honda rider Marco Simoncelli on the 10th lap of the 5.9-km course, with the Italian looking threatening in third place before skidding out.
"It was really tough conditions," said Stoner, the 2007 world champion who was starting his 150th Grand Prix in all categories and was quickest in practice on Friday and Saturday.
"Anything could have happened. We were quite lucky in this one that I stayed up and that Jorge had a crash."
Honda's Andrea Dovizioso was second, with Yamaha's Colin Edwards third.
Stoner's win lifted him 18 points above Lorenzo in the overall standings. Italy's Dovizioso stayed third but trimmed the gap to Lorenzo to 15 points with a third of the championship gone.
Results on Sunday at the British MotoGP at the 5.9-kilometer Silverstone circuit (rider, country, team, time):
MotoGP
1. Casey Stoner, Australia, Honda, 47 minutes, 53.459 seconds.
2. Andrea Dovizioso, Italy, Honda, 15.159 seconds behind.
3. Colin Edwards, United States, Yamaha, 21.480.
4. Nicky Hayden, United States, Ducati, 26.984.
5. Alvaro Bautista, Spain, Suzuki, 35.569.
6. Valentino Rossi, Italy, Ducati, 1:04.526.
7. Karel Abraham, Czech Republic, Ducati, 1:32.650.
8. Toni Elias, Spain, Honda, 1:51.938.
9. Hiroshi Aoyama, Japan, Honda, 1:52.350.
10. Loris Capirossi, Italy, Ducati, 2:03.312.
World Standings (After 6 of 18 races)
1. Casey Stoner, Australia, Honda, 116.
2. Jorge Lorenzo, Spain, Yamaha, 98.
3. Andrea Dovizioso, Italy, Honda, 83.
4. Valentino Rossi, Italy, Ducati, 68.
5. Dani Pedrosa, Spain, Honda, 61.
6. Nicky Hayden, United States, Ducati, 60.
7. Hiroshi Aoyama, Japan, Honda, 43.
8. Colin Edwards, United States, Yamaha, 37.
9. Ben Spies, United States, Yamaha, 36.
10. Karel Abraham, Czech Republic, Ducati, 33.
Moto2
1. Stefan Bradl, Germany, Kalex, 44 minutes, 10.236 seconds.
2. Bradley Smith, Great Britain, Tech 3, 7.601 seconds behind.
3. Michele Pirro, Italy, Moriwaki, 12.241.
4. Jules Cluzel, France, Suter, 17.271.
5. Scott Redding, Britain, Suter, 23.531.
6. Esteve Rabat, Spain, FTR, 28.661.
7. Yuki Takahashi, Japan, Moriwaki, 32.391.
8. Kenan Sofuoglu, Turkey, Suter, 34.662.
9. Yonny Hernandez, Colombia, FTR, 37.181.
10. Simone Corsi, Italy, FTR, 38.981.
World Standings (After 6 of 18 races)
1. Stefan Bradl, Germany, Kalex, 127 points.
2. Simone Corsi, Italy, FTR, 59.
3. Yuki Takahashi, Japan, Moriwaki, 56.
4. Andrea Iannone, Italy, Suter, 49.
5. Julian Simon, Spain, Suter, 49.
6. Thomas Luthi, Switzerland, Suter, 48.
7. Bradley Smith, Great Britain, Tech 3, 47.
8. Marc Marquez, Spain, Suter, 45.
9. Alex de Angelis, San Marino, Motobi, 42.
10. Michele Pirro, Italy, Moriwaki, 37.