Leclerc had fought off Lewis Hamilton from pole position, but the leading pair were the losers around the pit-stop window, with Vettel jumping from third to first by pitting first and making the most of the undercut.
Mercedes tried to keep Hamilton out longer, perhaps angling for a safety car or for the Ferraris to hit traffic, but the championship leader filtered back to fourth when he was serviced.
Three late safety cars did bunch up the leaders but crucially gave Vettel sufficient tyre life to hold off Leclerc and extend Ferrari's winning run to three races with his fifth victory around the Marina Bay Circuit, a new record.
Vettel had gone 392 days without taking to the top step of the podium, since Belgium last year, sparking questions about his future in F1 and his lasting talents.
An error in Monza last time out, with Leclerc going on to win, had ramped up the pressure further and the Monegasque seemed to have twisted the knife when he took pole position after Vettel made an error.
Much focus will fall on Ferrari's decision to effectively undercut their lead driver with the second car, but the Scuderia deserve credit for turning a 1-3 finish into a 1-2 finish, regardless of the order of the drivers.
And Vettel deserves significant credit for making is strategy work, especially his bullish work through traffic after pitting.
A bold wheel-banging move on Pierre Gasly was particularly eye-catching as Vettel showed his racing instincts remain intact.
Major questions will be asked of Mercedes, however, as they let a potential win slip through their fingers to fail to even get on the podium.
Hamilton had kept within a second of Leclerc in the opening stage of the race as the Ferrari man set a controlled pace, but he emerged two places and 11 seconds further down the road after staying out too long to pit.
That benefited Verstappen, who gained a place to continue Red Bull's run of podium finishes in Singapore, which stretches back to 2010.
Bottas and Alexander Albon completed the top six, with Lando Norris, Gasly, Nico Hulkenberg and Antonio GIovinazzi – who briefly led the race – rounding out the points-paying places.
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