The sensational podium tussle featured Rossi fighting back from an early mistake that dropped him to seventh, ultimately beating the Hondas of Marc Marquez and Dani Pedrosa to the runner-up spot.
Lorenzo held his pole advantage into the first corner and immediately disappeared up the road. An opening-lap lead of 0.6 seconds soon became two seconds and 5.9s by the end.
"Half an hour before the race I felt a little bit nervous so I had to really concentrate and relax on the grid," Lorenzo said.
"In the beginning it was hard to open the gap as Pedrosa didn’t want to let me get away, he tried to stay with me but after six or seven laps I opened the gap which made me more confident to keep my pace.
"I’m very happy for Yamaha and happy for Valentino as he has now passed two difficult years."
While the world champion was a class apart, there was no shortage of action in the battle to be second best.
Having qualified in the middle of the front row, Cal Crutchlow was elbowed back to fifth in the opening corners, as Pedrosa took second and Andrea Dovizioso's Ducati and Rossi surged to third and fourth.
Not keen to be behind ex-employer Ducati for long, Rossi twice dived past Dovizioso only to run wide.
While the first such error was mild, the second sent him over the Turn 1 run-off and down to seventh at the start of lap two.
Marquez had dropped to eighth on the opening lap but quickly sliced back up the order to get between Pedrosa and the recovering Crutchlow in their very close battle for second.
Rossi was stuck behind Stefan Bradl's LCR Honda until lap eight, by which time the works Hondas and Crutchlow were four seconds clear. Bradl crashed out soon after.
Though the podium battle appeared out of reach, Rossi was not to be denied.
By the time Marquez got ahead of Pedrosa for second with five laps left, Rossi was on the tail of this group.
He squeezed between Crutchlow and the pit wall for fourth in a cloud of dust, with the Briton then skittering over the run-off after sliding onto the Turn 1 kerbs.
Next on Rossi's list were the Hondas, both of which he passed within half a lap.
But the battle was not over. Marquez stayed with Rossi as Pedrosa fell away, and thrust back ahead into Turn 1 with a bold move two laps from home.
Rossi was soon in front again, but Marquez never gave up, staying on the seven-time champion's tail to the flag as he claimed a podium on his MotoGP debut.
"I’m more than happy, very happy indeed because it was my dream to come back with Yamaha," said Rossi.
"To arrive on the podium at the first race was my target from November and I put all my effort to arrive at the maximum here.
"In the end there was a great battle, especially with Marc for the second place. I’m so happy for me, for my team, for my friends and all my fans who stayed with me through two difficult years and also for Yamaha, to start the season with first and second place is not so bad.”
Behind Pedrosa and Crutchlow, Alvaro Bautista broke away from the Ducatis of Dovizioso and Nicky Hayden to take sixth.
Aleix Espargaro comfortably led the CRT pack home for Aspar. Tech 3's rookie Bradley Smith crashed out early.
QATAR MOTOGP RESULTS
1. Jorge Lorenzo (Spain) Yamaha 42:39.802
2. Valentino Rossi (Italy) Yamaha 42:45.792
3. Marc Marquez (Spain) Honda 42:46.003
4. Dani Pedrosa (Spain) Honda 42:49.275
5. Cal Crutchlow (Britain) Yamaha 42:58.566
6. Alvaro Bautista (Spain) Honda 43:01.950
7. Andrea Dovizioso (Italy) Ducati 43:04.157
8. Nicky Hayden (U.S.) Ducati 43:04.722
9. Andrea Iannone (Italy) Ducati 43:16.926
10. Ben Spies (U.S.) Ducati 43:24.710
11. Aleix Espargaro (Spain) Aprilia 43:29.611
12. Randy de Puniet (France) Aprilia 43:36.297
13. Hector Barbera (Spain) FTR 43:49.401
14. Yonny Hernandez (Colombia) Aprilia 43:50.544
15. Hiroshi Aoyama (Japan) FTR 43:53.402