With Lorenzo never looking like relinquishing his advantage in the closing stages, he crossed the line 5.672 seconds ahead of Rossi.
The 23-year-old, who has 70 points to Rossi's 61, celebrated his latest win by pulling up a folding chair in front of one of the circuit's big screens and munching a bucket of popcorn.
"Passing Valentino wasn't so easy because he was braking so deep and I had to be very patient, something that I might not have managed one year ago," said the Spaniard after his first back-to-back MotoGP wins.
Lorenzo celebrates French MotoGP win with popcorn
"Finally I overtook him but I didn't expect to be able to get away like that."
Rossi admitted afterwards that he had not expected to be able to hold off his rival.
"I did a great start and I tried to stay in front because I understood from the bike that I didn't have the same pace," he said.
"I knew there was no way to stay in front for 28 laps."
Rossi said his main problem was with the set-up, with his bike lacking grip under acceleration.
It was the first time since 1980 that Japanese manufacturer Yamaha has started the season with three successive wins in the top category.
MotoGP result (round 3 of 18):
1 J Lorenzo (Spa) Yamaha 44 mins 29.114 secs 2 V Rossi (Ita) Yamaha 44:34.786 3 A Dovizioso (Ita) Honda 44:36.986 4 N Hayden (US) Ducati 44:38.460 5 D Pedrosa (Spa) Honda 44:41.727
1 J Lorenzo (Spa) Yamaha 70 points 2 V Rossi (Ita) Yamaha 61 3 A Dovizioso (Ita) Honda 42 4 D Pedrosa (Spa) Honda 40 5 N Hayden (US) Ducati 39
1 T Elias (Spa) Moriwaki 43 mins 29.277 secs 2 J Simon (Spa) Suter 43:30.613 3 S Corsi (Ita) Motobi 43:32.108 4 A Iannone (Ita) Speed Up 43:34.157 5 G Talmacsi (Hun) Speed Up 43:42.570
Selected other: 11. Scott Redding (Britain) Suter 43:53.236
1 T Elias (Spa) Moriwaki 63 points 2 S Tomizawa (Jpn) Suter 45 3 S Corsi (Ita) Motobi 35 4 J Simon (Spa) RSV 28 5 S Gadea (Spa) Pons Kalex 26
1 P Espargaro (Spain) Derbi 41 mins 52.280 secs 2 N Terol (Spain) Aprilia 41:53.237 3 M Marquez (Spain) Derbi 41:56.708 4 E Vazquez (Spain) Derbi 41:57.016 5 Bradley Smith (Britain) Aprilia 41:57.423
1 N Terol (Spain) Aprilia 65 points 2 P Espargaro (Spain) Derbi 63 3 E Rabat (Spain) Aprilia 34 4 E Vazquez (Spain) Derbi 33 5 M Marquez (Spain) Derbi 32
Selected others: 6 B Smith (Britain) Aprilia 32 13 D Webb (Britain) Aprilia 12
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