Yamaha rider Lorenzo started from pole and led for the opening laps before Stoner's Honda powered past to take a lead that the reigning champion did not look like relinquishing until the latter stages.
After establishing a cushion of around two seconds at the front, Stoner's bid fell apart in the closing laps as the physical toll of the race hit his hopes and dropped him to an eventual third-placed finish.
Stoner revealed afterwards that he had been suffering from 'arm pump', a condition common among motorcycle racers that causes muscular swelling in the arm as a consequence of gripping the handlebars.
The problem first dropped him behind Lorenzo into second, and then to third at the flag as team-mate Dani Pedrosa swept past to claim the runner-up spot.
Fourth place went to Britain's Cal Crutchlow.
Lorenzo was happy to take the victory however it came about, and was delighted to make a perfect start to his bid to wrest back the championship that Stoner claimed from him last season.
"I put everything I have into the track," Lorenzo told BBC Sport. "Casey was very strong at the beginning, opened a gap. Lucky for us he dropped his pace.
"I'm very grateful to Yamaha. They did a big job this winter."
Stoner looked well set for victory after battling back from the shock of seeing Pedrosa beat him into the first corner despite the Spaniard starting seventh on the grid.
From second place on the grid, Stoner should have been watching the back of Lorenzo through turn one but instead he found Pedrosa barring his way after his sublime getaway.
The reigning champion was not bottled up for long, however, passing Pedrosa into turn one at the start of lap three and then doing likewise to Lorenzo on the next tour.
But victory was destined to be snatched away as his physical condition deteriorated, although Stoner was sanguine in defeat.
"We were by far the fastest out there," he said. "After four laps I started getting really bad arm pump. By the end of the race I could not grip anymore. I could not keep up the pace.
"But in general we're happy. There's a lot of positives to take from this. We're pretty happy with the pace."
Behind the top three, Crutchlow equalled his best finish in MotoGP as he came home in fourth place for Tech 3 Yamaha. The Briton, who qualified in third but was immediately dropped by the fast-starting Pedrosa, came home just ahead of Andrea Dovizioso after a race-long duel between the new team-mates.
Nicky Hayden was the first of the Ducatis home in sixth ahead of Alvaro Bautista (Gresini Honda), Stefan Bradl (LCR Honda) and Hector Barbera (Pramac Ducati), while Hayden's team-mate Valentino Rossi finished down in 10th after surviving an early off-track excursion.