Starting from pole-position for the third race in a row, Vettel extended his lead over Lewis Hamilton to over eight-seconds before the chasing Brit made his first pit-stop.
Sebastian Vettel believes he had no choice but to try to pass Valtteri Bottas for the lead after the safety vehicle restart on Lap 48 despite the move losing him a podium finish.
As luck would have it, a safety auto was triggered on Lap 40 when Red Bull Racing teammates Max Verstappen and Daniel Ricciardo collided with each other, allowing Bottas to switch to new ultrasoft tires and maintain his race lead.
Carlos Sainz finishing fifth for Renault and Charles Leclerc sixth for Sauber, his first points finish. A reasonably early pit stop gave him warm soft tyres with 20 laps to go - which gave him the edge he needed to cling on until the chequered flag.
The two Red Bulls driven by Max Verstappen and Daniel Ricciardo fought all race for fourth place. "If we can manage that, I think we've got a real good handling race auto".
Verstappen lost the place into Turn 1 just after mid-distance but got back ahead by pitting a lap later than Ricciardo, then swiftly came under attack as Ricciardo picked up a huge tow on the run down to Turn 1. Five laps later with fresher tires, Ricciardo attempted to cleanly pass his teammate, but Verstappen blocked the move leading to contact between the two Red Bull drivers.
Romain Grosjean sent his Haas careering into the wall to reduce the laps for racing further, and the misfortune of Vettel and Bottas meant it was Hamilton who somehow came out on top for his first podium in Azerbaijan and Mercedes' maiden win of 2018. Hulkenberg's race came to an end when he lost the rear of his auto at Turn 5 and hit the wall, while Sainz dropped down the order with an early pit stop but eventually went on to finish fifth following retirements further ahead.
For Red Bull it was an afternoon that will require a stern debrief with their drivers.
Hamilton's early pit stop gave him good warm tyres for the closing stages, even though those final laps were interrupted by the safety vehicle again. Sergio Perez ("Force India") - +4,0244. It is always going to be an issue and this time it is just unlucky.
Vettel backed the field up hugely at the restart and kept everyone bottled up until the last possible moment before the final safety vehicle line.
Romain Grosjean crashed under the safety vehicle on lap 42, sliding into the wall while weaving in an attempt to heat up his tires. Hamilton and Raikkonen did the same, setting up a sprint race to the finish between the top four drivers. Lance Stroll ("Williams") - +12,5469.
Ricciardo braked late and ran into the back of the younger man, who was attempting to cut back across and prevent his progress.