Vettel was joined on the podium by 2017 World Champion Lewis Hamilton, who finished second - and was passed by the Ferrari in controversial fashion under virtual safety car, while Kimi Raikkonen rounded out the top 3.
Australia's Daniel Ricciardo finished in fourth, rising from eighth on the starting grid to work his way through the field and nearly snag his first ever home podium.
Ricciardo was able to rise through the pack early, as he made easy work of the Renault of Nico Hulkenberg who started in front of him.
When his Red Bull team-mate Max Verstappen spun out early in the race, it gifted yet another position to Ricciardo - much to the chagrin of his team garage.
However, the hometown hero was having a tough time getting past the Haas pair of Romain Grosjean and Kevin Magnussen - who were sitting in 4th and 5th respectively and looking very impressive in the early stages of the race.
Unfortunately for the Haas drivers, it only took five minutes of madness to see them both drop out of contention - as similar incidents forced both drivers out of the race, as the Haas pit crew were unable to secure the tyre during a change-over and prematurely ended their day in the process.
These issues ultimately saw Grosjean stuck on track and a virtual safety car was called - and an opportunistic Ferrari team saw a chance to bring Sebastian Vettel into the pits while Lewis Hamilton was forced to stay beneath track limits, allowing him to undercut the Mercedes and take the race lead without ever passing Hamilton.
When the race resumed - there was a relentless battle for the lead between Vettel and Hamilton, and also for third between Raikkonen and Ricciardo...but it was the Ferrari's who won both of those battles in the end, securing the race win and two spots on the podium in the process.
Fernando Alonso of McLaren was next to finish - crossing the chequered flag in fifth, while Max Verstappen of Red Bull finished sixth after recovering from his early spin-out.
Renault's Nico Hulkenberg finished eighth, while Mercedes' Valtteri Bottas and McLaren's Stoffel van Doorne rounded out the Top 10 for the day.