Hayden's team-mate Valentino Rossi
began his 200th premier-class grand prix from a lowly 13th on the grid and see-sawed between tenth and eleventh for the first third of the race.
The struggling Italian superstar then formed part of a five-way fight for ninth during the middle stages, alongside Pramac Ducati's Hector Barbera, Lorenzo's team-mate Ben Spies, Cardion AB Ducati's Karel Abraham and the top CRT of Randy de Puniet.
Rossi and Barbera later pulled away from sixth-on-the-grid Spies, suffering race day woes for the second event in succession, with Rossi eventually crossing the line a fraction ahead of the Spaniard.
Abraham crashed and re-joined while de Puniet failed to finish, the frustrated Frenchman parking his Aspar Aprilia on the penultimate lap, handing his safe twelfth and top CRT honours to team-mate Aleix Espargaro.
Fellow CRT riders Danilo Petrucci (Ioda), Mattia Pasini (Speed Master) and Ivan Silva (Avintia) completed the point scorers.
Forward Racing's Colin Edwards, the top CRT rider in Qatar, began the race in last place, where he remained until Abraham's fall.
Lorenzo now leads the early championship standings by four points over Stoner.
Round three of the 2012 MotoGP World Championship, the Portuguese Grand Prix at Estoril, takes place next weekend - when the weather could be equally changeable.
1. Casey Stoner
2. Jorge Lorenzo
3. Dani Pedrosa
4. Cal Crutchlow
5. Andrea Dovizioso
6. Alvaro Bautista
7. Stefan Bradl
8. Nicky Hayden
9. Valentino Rossi
10. Hector Barbera
11. Ben Spies
12. Aleix Espargaro
13. Danilo Petrucci
14. Mattia Pasini
15. Ivan Silva
16. Colin Edwards
17. Karel Abraham