Verstappen became the first driver this year to put a car without a Mercedes engine on pole, with Ferrari's Lewis Hamilton joining him on the front row at the Sepang International Circuit.
Championship leader Kimi Antonelli could only manage fourth-fastest for Mercedes but will move up to third due to a five-place grid penalty for Red Bull's Isack Hadjar.
Antonelli's teammate George Russell was eighth fastest in qualifying and will start seventh on the grid.
"Very difficult to understand, we have been a little bit caught out on Friday with some car behaviour we didn't see all year. But you can say it is very hot and the tarmac is very different to other tracks," Mercedes boss Toto Wolff told Sky Sports.
"We looked good in (FP3), at least with Kimi, but then a return to those issues. We are very draggy, losing time on the straights to Max, and then we have understeer in the low-speed (corners), which we haven't seen all year."
The session was a major blow to Antonelli and Russell, who is second in the championship and was riding a wave of confidence after reducing his teammate's lead to 66 points in Azerbaijan last weekend.
Antonelli seemed to have found his rhythm when he topped the final practice session on Saturday but could not squeeze anything more out of the car in Q3.
"All in all, we have to be happy because it could have been much worse. We'll focus on tomorrow," said Antonelli, who leads the championship with 302 points while Russell is second, 66 points behind.
Hope remains for Russell
Russell said they had not made improvements since the first practice session and tyre degradation was hurting Mercedes more than their rivals.
"It's a very demanding circuit on the tyres, the tarmac is all broke up, it's extremely rough, it's so hot out there, and the tyres are going through hell," Russell said.
"For whatever reason, it seems to be affecting us far more than others."
Wolff remained confident in the potential of the upgrade package.
"Something else is going on which we need to understand. We need to look through the data and put our heads together as we still believe the upgrades work," he added.
"We expected to be three-tenths (of a second) forward, and we are four or five backwards."