The Red Bull-backed racer led the way after the first runs, where he was one of the last cars to return to the pits for a new set of tyres.
That lap was not enough for pole though, as Jazeman Jaafar and then Nikolay Martsenko took top spot.
Martsenko improved again on his next flying lap to increase his margin over the field to half a second over Sainz with just three minutes remaining, but the Spaniard moved to the top by half a tenth on his next lap.
While Martsenko was unable to improve again, Sainz set another lap just 0.017s shy of his pole time.
There was a change for second place right at the end of the session, as Oliver Rowland moved into second as the last car to pass the chequered flag, missing out on pole by just 0.018s.
Late laps from Roberto Merhi and Zoel Amberg enabled them to complete the top five, just ahead of 2013 Formula Renault Eurocup champion Pierre Gasly, who is one of two drivers to currently share the championship lead with Sainz.
The other co-championship leader, Will Stevens, suffered a session to forget as he scrapped towards the bottom of the times throughout.
The Caterham F1 junior - whose Strakka Racing team has struggled for pace on new tyres so far this year - was 20th fastest out of the 21 cars after the first runs, and he could only recover to 15th with his final lap of the session.
"It's the same problem as always," said the Briton. "Yesterday on old tyres we were fastest, but we can't get the car to work on new tyres.
"I'm sure we'll make up places in the race, but this isn't where we want to be starting from. Right now we don't have the answer [on new tyres]."
Pos Driver Team Time Gap Laps
1. Carlos Sainz Jr DAMS 1m40.418s 14
2. Oliver Rowland Fortec 1m40.436s +0.018s 13
3. Nikolay Martsenko Comtec 1m40.474s +0.056s 14
4. Roberto Merhi Zeta Corse 1m40.581s +0.163s 11
5. Zoel Amberg AVF 1m40.611s +0.193s 14
6. Pierre Gasly Arden 1m40.624s +0.206s 13
7. Marlon Stockinger Lotus 1m40.692s +0.274s 14
8. Pietro Fantin Draco 1m40.702s +0.284s 15
9. Sergey Sirotkin Fortec 1m40.709s +0.291s 13
10. Will Buller Arden 1m40.741s +0.323s 14
11. Jazeman Jaafar ISR 1m40.823s +0.405s 13
12. Matias Laine Strakka 1m40.894s +0.476s 13
13. Matthieu Vaxiviere Lotus 1m41.193s +0.775s 14
14. Norman Nato DAMS 1m41.198s +0.780s 12
15. Will Stevens Strakka 1m41.201s +0.783s 14
16. Meindert van Buuren Pons 1m41.244s +0.826s 13
17. Luca Ghiotto Draco 1m41.277s +0.859s 13
18. Marco Sorensen Tech 1 1m41.344s +0.926s 13
19. Roman Mavlanov Zeta Corse 1m41.648s +1.230s 12
20. Oliver Webb Pons 1m41.649s +1.231s 13
21. Beitske Visser AVF 1m42.240s +1.822s 13
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