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.
After the retirement of compatriot Mark Webber, the Australian was promoted to the senior Red Bull team in 2014.
The teams were given an extra 43 kilograms to play with this season due to brand new technical regulations introduced by the FIA.
When the lights went out at Jeddah, the Mexican made history by becoming his country's first-ever F1 polesitter.
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.
The Monegasque driver set a best time of 1:29.735 to edge out defending world champion Verstappen by 0.033s.
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.
As per a report, a spokesperson for Red Bull said that the issues in both cars were due to a vacuum created in the fuel system.
Verstappen seemed to lose his cool completely on the team radio and expressed his disappointment with how things turned out.