Hamilton had been on pole for six races in a row until Bottas broke the sequence in Bahrain and Wolff said Mercedes appeared to be still slightly ahead of Ferrari on single lap pace. "Apologies to the team but I tried the best I could to recover it and we still got good points for today", the Guardian quoted Hamilton as saying of his error.
Vettel started third on the grid, but on the first lap itself on turn one managed to squeeze past Lewis Hamilton and eventually managed to jump pole-sitter Valtteri Bottas in the first round of pit stops after a safety auto period.
The two teams had been very evenly matched in race pace but Ferrari's aggressive pit strategy gave Vettel the advantage, and when Hamilton pitted under the safety auto he was too slow into the pit entry and took a five-second penalty.
Vettel's 44th win lifted him to 68 points, with Hamilton second on 61."Yes guys, that's what I'm talking about", whooped the German, who was helped by the safety vehicle being deployed after his first pitstop with the Mercedes duo still out, as he took the chequered flag.
He went on to pass the Australian before serving his penalty during his second pit stop before finally passing Bottas in the closing laps and finishing behind Vettel.
"I know that gap that was there doesn't just come from driving".
The third spot on the podium was occupied by the second Mercedes driver - Valtteri Bottas.
The safety vehicle came out, after which the two Mercedes drivers pitted for fresh tires.
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Asked about the team's request to let Hamilton through, Bottas admitted: "Honestly, as a racing driver, it is maybe the worst thing you want to hear, but that's how it is". As a team we didn't achieve that, Ferrari did a better job, so I'm leaving here with a bit of a unusual feeling, because I don't know why the pace was so poor. The Brit ended up losing the race by 6.6 seconds and did apologise for that unnecessary mistake which he could have avoided.
Hamilton was catching the German on every lap but ultimately ran out of time and finished nearly seven seconds behind. I don't know what to say, but that's not why we exist.
"Possibly I would have been in a better position", Hamilton said, "but that's all ifs and buts".
Most of the drivers made a minimum of three stops in 2016 but, in a very short space of time this time around, they only headed into the pits twice.
Fernando Alonso was the last classified finisher in P14 for McLaren, pitting with three laps to go due to an engine failure. Personally, it is tough for me, but that's life.
"I didn't have enough pace today and we need to find the reasons why".
Germany's Nico Hulkenberg was ninth for Renault, that team's first points of the year, and French rookie Esteban Ocon bagged the final point for Force India.