This was the German rider's first Grand Prix victory in 392 days. However, he started the competition in the second row, having finished Saturday's qualifying in the third place, Efe reports.
"Obviously, I'm a bit sweaty! Very happy, great race," Vettel said after the race, the 15th of the season's 21 events.
"The start of the season was difficult for us, but now we've started to come alive," Vettel added.
Even though race officials deployed the safety car three times at Marina Bay, 32-year-old Vettel, a five-time world champion, was always in the lead after the three restarts.
Monaco's Charles Leclerc (Ferrari), who started the race from the pole position, finished in second place because Ferrari team officials decided to grant the German rider first place.
Leclerc, who has claimed three consecutive pole positions this season, could have earned his third successive race win on Sunday, having emerged victorious at the Italian and Belgian GPs.
The 21-year-old rider was surprised by Ferrari's strategy, expressing shock on the team's radio.
"It's always difficult to lose a win like that," Leclerc said following the race.
"It's the first one-two (finish for Ferrari) for the season, so the whole team deserves it," he added.
Red Bull's Dutch rider Max Verstappen completed the podium after defending the third spot in the final stretch, while Briton Lewis Hamilton (Mercedes) came in fourth, ahead of his Finnish teammate Valtteri Bottas.
"The whole race went well... I started to struggle with the tires so we boxed and that became a good call as we undercut Lewis. In general, happy to be on the podium," Verstappen said.
Thai Alexander Albon (Red Bull), Briton Lando Norris (McLaren), Frenchman Pierre Gasly (Toro Rosso), German Nico Hulkenberg (Renault) and Italian Antonio Giovinazzi (Alfa Romeo) completed the list of top-10 finishers.
( With inputs from IANS )