Daruvala had led the majority of the session, carrying on the fine pace he showed in practice, but Tsunoda spoiled his party at the last minute to narrowly take pole position.
When the 30-minute long session began, Prema driver Mick Schumacher was the first to set a competitive laptime - a 1m49.924s - but he was almost immediately displaced from the top of the timesheets by fellow Ferrari junior Robert Shwartzman, who went three tenths quicker with a time of 1m49.634s.
Daruvala and the Hitech of Nikita Mazepin then traded the quickest times, before the Indian driver asserted his authority with a 1m49.068s - the fastest lap of the weekend so far.
When the second runs began, Daruvala managed to find even more time, becoming the first driver to break the 1m49s barrier with a time of 1m48.990s.
Tsunoda managed to improve to 1m49.284s to provisionally make it a Carlin 1-2, before gaining a whopping seven tenths to snatch pole position from Daruvala.
Daruvala himself managed to find a lot of time on his final flyer, but ultimately fell just 0.006s short of beating his teammate.
Championship leader Schumacher qualified third with his late effort of 1m48.883s, with Callum Ilott completing the second row for Virtuosi.
Ilott had dropped outside the top 10 after encountering traffic on his first run, but managed to move up to fourth with a late flyer of 1m49.047s.
Practice pacesetter Luca Ghiotto finished as the top Hitech driver in fifth, beating the ART of Christian Lundgaard by just 0.032s.
Shwartzman enjoyed improving qualifying form to finish seventh, ahead of the Charouz of Jack Aitken and Virtuosi driver Guanyu Zhou.
Mazepin was unable to trouble the leaders in the second half of qualifying, his early effort of 1m49.474s leaving him 10th in the final order.
Red Bull protege Juri Vips was classified as the top DAMS driver in 11th, four spots clear of HWA debutant Jake Hughes.