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The title gap blew out to 62 points with three rounds remaining and 86 points still to be won.
Horner, whose team is currently leading both championships, had denied the accusations.
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.
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.
The Dutch driver took the chequered flag 22.4 seconds clear of his team mate Sergio Perez driving a similar RB20.
Red Bull has said the investigation report will remain confidential.
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