The Red Bull-backed driver slashed his deficit to second-placed rival Theo Pourchaire to just 10 points in the overall standings after taking his fifth podium from six rounds last time out in Baku.
The reigning world champion was more than six tenths clear of surprise front-row star Fernando Alonso of Alpine and third-placed Carlos Sainz of Ferrari.
Tsunoda will take a completely new engine - with fresh internal combustion engine, turbocharger, MGU-K, MGU-H, control electronics and energy store - plus a fifth exhaust of the season.
Max Verstappen led a Red Bull one-two in the Azerbaijan Grand Prix after retirements for Ferrari's Charles Leclerc and Carlos Sainz, giving Mercedes' George Russell P3 at Baku.
Charles Leclerc took pole position with a stunning lap in qualifying for the 2022 Azerbaijan Grand Prix, as Sergio Perez put himself on the front row in P2.