On Lap 39 of 58, Verstappen was forced to retire, leaving him in sixth place in the drivers' standings, with only 25 points for his Jeddah victory.
Sergio Perez of Red Bull finished second, with Mercedes' George Russell rounding out the podium.
The Monegasque driver put in a scintillating final flying lap which saw him record a time of 1:17.868s.
Medium-tyred runs were first in FP2, with Sainz, the FP1 leader, setting the early pace, before softs were fitted and Leclerc jumped to P1.
If the first two races are any indication, Ferrari will have to race in 2022 with their own power unit, as even their customer teams appear to be enjoying straight line speed.
In a much-improved Ferrari package, Leclerc has taken a victory and a P2 in the first two races of the season, and is now leading the drivers' standings.
With a second wind in the closing stages, Charles Leclerc set the fastest lap, but reigning champion Max Verstappen kept him at bay.
The Ferraris of Charles Leclerc and Carlos Sainz secured P2 and P3 respectively while reigning champion Max Verstappen could only manage P4.
On the soft compound tyres, Leclerc, who didn't break cover until halfway through the session, set a time of 1m 30.772s in the closing stages.
While Sainz is ecstatic to have a car to race, he recognises that staying there and competing on the development front will be difficult.