The Japanese Formula 3 frontrunner became the first driver all weekend to drop below the 1m41.000s barrier as he set a 1m40.840s with just one minute of the 30-minute session remaining.
Palou, who is replacing the unavailable Nelson Mason at Teo Martin Motorsport this weekend, almost failed to make qualifying as his car had to be towed to the pits for the start of the session.
The lack of drive proved to be a temporary issue as he set a time 0.345 seconds faster than Diego Menchaca, who rekindled the form he had in Friday morning's practice session to claim a spot on the front-row.
Championship leader Pietro Fittipaldi struggled to make his mark in the second qualifying session. His time of 1m41.602s looked set to secure the Lotus driver his ninth pole position of the season, but a flurry of fast laps in the closing minutes relegated him to sixth.
The session wasn't much kinder on his Lotus team-mate Rene Binder. Binder, who has been off the pace for most of the weekend, will be starting ninth as late improvements from seventh-placed Alfonso Celis and eighth-placed Yu Kanamaru pushed the Austrian down the order.
Towards the front of the field, Matevos Isaakyan was unlucky not to find himself on the front-row as his 1m41.257s was just 0.072s slower than Menchaca's best. However, he was just 0.005s faster than fourth-placed Roy Nissany, the latter enjoying his best session so far at the Nurburgring.
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