Vettel now leads Hamilton by 17 points after two of the 21 races.
Verstappen lasted three laps longer than Ricciardo before retiring with gearbox damage as a result of having to drive an entire lap on three wheels and a damaged rim after the impact with the Briton. A Virtual Safety Car was called so the Red Bull could be recovered, cooling things down after a heated start.
Hamilton, meanwhile, was picking his way up the order, soon moving into sixth place after heading down the main straight alongside Nico Hulkenberg, Alonso and Esteban Ocon, overtaking them into Turn 1.
Bottas stayed out for two more laps and changed to mediums.
Kimi Raikkonen rues Q3 traffic after missing out on Bahrain pole
In a further boost for Ferrari, the aging Kimi Raikkonen has looked sharp all weekend, leading the second and third practice. Bottas was happy to bounce back after his confidence-sapping crash in qualifying in Australia two weeks ago.
Not only did this force the Finn out of the race, but it also lead to the injury of Ferrari pit crew member Francesco, to whom we wish a speedy recovery. Although the German driver looked steady behind the wheel, his mind was racing nearly as fast as Bottas' Mercedes behind him.
Hamilton's Mercedes teammate Valtteri Bottas crossed the line in second after the other Ferrari of Kimi Raikkonen, which started second, failed to finish. Bottas had a flawless drive right till the end, bringing in the gap of eight seconds from the German, down to under a second at the last lap, but unfortunately ran out of laps before making the final overtake. Vettel would have been on fresher tyres and in a position to push had he done so, but in the end Ferrari felt it was better to keep their man out on track and attempt to retain the lead to the flag.
The Italian later posted another of him standing on crutches.
Raikkonen got passed on the first corner by Bottas, but Vettel held his ground.
"With Bottas' pace I thought he would catch me".
Australia smash team pursuit world record as England take silver
And Stephanie Morton and Kaarle McCulloch, who made up the women's team sprint pair, won their event, also beating NZ. Gold medalists Shayna Jack, Bronte Campbell, Emma McKeon and Cate Campbell of Australia celebrate on the podium.
Ferrari drafted Raikkonen into the pits at the end of Lap 35 to put him onto a set of Supersofts, hoping their added performance would give him the chance to jump Hamilton.
Cigarini fractured the shinbone and fibula on his left leg after being struck during a botched pit-stop, with Ferrari driver Raikkonen given the signal to go before the left rear tyre had been replaced.
Vettel was now left alone to fight at the front of the pack against both Mercedes drivers, but began to up his pace to extend the gap out to Bottas.
Raikkonen was forced to retire from the race following an issue with his rear left tyre. That was the original plan and then we diverted and the tyres I tried to make them last and nurse them as much as I can, and it worked. Raikkonen came in a lap later, with the Ferraris falling to P3 and P4 before leader Bottas stopped on lap 20.
Stunning Sagan adds Paris-Roubaix to legend
The team said Goolaerts died "in the presence of his family members and loved ones, who we keep in our thoughts". Goolaerts crashed 109km into the 257km race and was found unconscious by race doctors.
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