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The 39-year-old Mercedes driver's last win before Silverstone was in Saudi Arabia on December 5, 2021, and Sunday was a record-extending 104th of his career.
McLaren's Oscar Piastri finished second with Ferrari's Carlos Sainz third at Spielberg's Red Bull Ring.
Red Bull's Dutch driver has extended his championship lead to 69 points.
The Dutchman grimly hung on to claim his sixth victory from nine races this season and the 60th of his Formula One career.
The victory extended Verstappen's championship lead to 48 points, with Leclerc now his closest rival after Red Bull's Sergio Perez started 11th and finished only eighth.
The comfortable victory from pole position at a Shanghai circuit that last hosted a Grand Prix in 2019 was Verstappen's fourth in five races in 2024 and came after he also won the season's first Saturday sprint.
Verstappen, who becomes only the second driver to win three consecutive Japanese Grands Prix alongside seven-time world champion Michael Schumacher, now has a 13-point lead in the drivers standings over Perez.
It was Verstappen's first DNF (did not finish) since retiring from Albert Park in the 2022 race and ended his run of race wins at nine.
Sergio Perez was runner-up under the Jeddah Corniche floodlights, last year's winner taking the chequered flag 13.643 seconds behind his triple world champion teammate who now has a 15-point lead in the standings.
Verstappen senior also denied involvement in the anonymous email.