With Jorge Lorenzo's Yamaha just behind the Australian's Honda in second and Nicky Hayden putting his Ducati third, all three works teams had a presence in the top three at the end of the close-fought session.
Ben Spies had set the pace for most of the first half of practice on the other works Yamaha, before his 1m57.606s was pipped by just 0.005 seconds by the satellite Tech 3 Yamaha of Cal Crutchlow.
Spies regained the top spot with a 1m57.285s six minutes later, though he was then swiftly deposed by a 1m57.256s from Stoner.
The final few minutes saw a flurry of changes, as first Spies returned to the head of the list with a 1m56.982s, then Lorenzo popped up to first on a 1m56.648s, before Stoner delivered an unbeatable 1m56.474s.
Hayden had briefly been second behind Lorenzo, before Stoner's time pushed them back to second and third, ahead of Spies.
Dani Pedrosa made late gains to take fifth on the other factory Honda, as Crutchlow's impressive evening ended with sixth place.
Alvaro Bautista (Gresini Honda), Andrea Dovizioso (Tech 3) and Hector Barbera (Pramac Ducati) filled seventh to ninth positions, while Valentino Rossi's year kicked off with a quiet 10th for Ducati.
Randy de Puniet was the fastest CRT runner for Aspar, though only after swapping places with Forward Racing's Colin Edwards a few times. Moto2 graduate Michele Pirro was right behin them despite his lack of pre-season mileage on Gresini's CRT entry.
Under Qatar's unique four-day schedule, MotoGP's second and third practice sessions both take place on Friday night, before qualifying on Saturday.