Formula One's logistics partner DHL holds an annual fastest pitstop award with points accrued over the season. Red Bull is leading Williams in the standings after 11 of 21 races, with Ferrari third.
It was the second race in a row that the expertly-choreographed Red Bull mechanics had broken the record, with a 1.91-second pitstop for French driver Pierre Gasly at the British Grand Prix two weeks earlier.
Verstappen made five pitstops in a chaotic race at Hockenheim, and Gasly four, with the fastest coming on the 46th of the 64 laps.
Red Bull team boss Christian Horner sent chief mechanic Phil Turner up to the podium to collect the winning constructor's trophy.
"The pit stop crew were unbelievable today," said Horner.
Hamilton's slowest lasted some 50 seconds and came just after he had hit the barriers, with some of his mechanics changing the front wing while others swarmed around uncertain which tyres to fit.