Bottas's team mate and reigning world champion Lewis Hamilton, who had started ninth after a five-place grid penalty for an unscheduled gearbox change, finished third.
Vettel held off the charge of Mercedes' Valtteri Bottas to take victory in his 200th grand prix, but the occasion was soured after a member of Raikkonen's pit crew was taken to a medical center after an incident during lap 36 of the race. In an ironic twist, Red Bull's feeder team Toro Rosso had arguably the result of the day - with French driver Pierre Gasly driving superbly to finish a career-best fourth.
Hamilton, meanwhile, escaped undamaged from his scrape with the Red Bull driver and made rapid progress of his own, climbing to fourth by lap eight. The incident brought out the red flag, which delayed the session for no more than five minutes while marshals pulled out Verstappen's vehicle.
Verstappen had already set a time fast enough to get into Q2, but the auto was too damaged to take any further part in the session. I go when the light is green...
"We'll see how that is reliability-wise but car-wise they are on par with us and this weekend they are ahead of us".
Coming in for his second stop, Raikkonen's left-rear tire was slow coming off and Ferrari had yet to remove it when the vehicle was dropped from the jacks and the pit lane light went green, leading Raikkonen to pull away and hit a mechanic working on his stuck tire. The Finn also hit and injured one of his mechanics as he pulled away. The team subsequently tweeted that he had been transported to a nearby hospital for further treatment.
Back out, Vettel quickly caught and past Hamilton on his fresher rubber and it was those few laps which would take the Briton out of the battle for the win as he emerged over 20 seconds behind.
Vettel took off cleanly to hold the lead into the first turn but Bottas did what was required and jumped Raikkonen to claim second.
This left Hamilton to make up places and after slipping to 10th he regained ninth and then passed Alonso, Hulkenberg and Ocon in one move.
Vettel's win pushed him up to 50 points in the drivers' standings, 17 ahead of Hamilton, with Bottas third on 22 points.
In the lead, Hamilton was 5.3 seconds clear of Vettel after 22 laps, an advantage trimmed to half a second by lap 25 with Bottas five seconds adrift in third.
Vettel and Bottas - who jumped Kimi Raikkonen at the start - both ran one-stop strategies, but went in a different direction with their choice of compounds.