Verstappen and Ricciardo had carved their way to the top after an inspired gamble by Red Bull team principal Christian Horner to haul both of his drivers in for fresh tyres after Brendon Hartley and Pierre Gasly tangled and the safety vehicle was sent out.
Vettel's two-race winning start was ended by Ricciardo, who started sixth on the grid and was not in the picture in the first half of the race. Verstappen was ahead of teammate Ricciardo but he ran wide after an overtaking move on Hamilton went wrong, which allowed his teammate ahead.
Max Verstappen admitted that he was "disappointed with [himself]" after a Chinese Grand Prix in which he received a ten-second penalty for a collision with Sebastian Vettel.
Raikkonen took a few good looks but ultimately was just under 0.8 seconds behind Bottas at the finish with Verstappen another 0.8 seconds behind him on the road.
Pilot Red bull Daniel Riccardo in bright style became the victor of the third race of the season in Formula 1.
Ricciardo now sits fourth in the Drivers' Championship, 17 points behind leader Vettel.
He finally picked off race leader Valtteri Bottas, passing the Finn with inches to spare, to set up his win.
Earlier frantic opening lap had seen Verstappen to jump up to third, with Lance Stroll also one of the earlier benefactors of the early stages.
Until the 31 out of 56 laps around the 5.451km, 16-turn Shanghai International Circuit the Chinese GP had looked to be a tense tussle between Mercedes' Valtteri Bottas and Ferrari's Sebastian Vettel.More news: Ashwin to return against Chennai Super Kings
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The collision that saw the safety vehicle deployed was deemed to be Pierre Gasly's fault, and he was given a ten-second penalty.
"In the end we would have needed the soft tyres to really go for it". "There's over 700 members in our team and I think what we've demonstrated this weekend is that it all has to work in unison and the effort that went in yesterday to change that engine in two hours - an hour quicker than we've ever achieved it - and then the double pit stops for the first stop and then under the safety auto".
Daniel Ricciardo at the post-race press conference: "Once I was aware we had the pace I wasn't going to let it slip". Every win I've had has been in a similar circumstance.
"I enjoyed it, it makes a bit sweeter than just cruising past on the straight so that was a lot of fun".
"It was hectic, I heard safety vehicle [was being called] in T14". Yesterday and today was a disaster on my side. I knew there would be enough room, the tyres had enough grip.
"It is disappointing. We gave it everything we had", said Bottas.
"This is racing, these things happen".
"When you compete in more races you should get more clever - especially when you want to win or challenge for the championship - but he is going the other way".