Vettel beat Mercedes' Lewis Hamilton after a 5 second time penalty saw the Briton lose ground and eventually hampered his chances of victory. Hamilton, who entered the pits soon after slowed down in the pit lane so as to allow Mercedes enough time to send Bottas on his way before Lewis came along. Apologies to the team but I tried the best I could to recover it and we still got good points for today.
Hamiltons hopes were also hit when the British driver was given a five-second time penalty early into the race for driving too slowly in the pit lane and holding up Red Bulls Daniel Ricciardo, who finished fifth.
After the safety auto, Vettel came out in the lead where he remained after the next round of pit stops, despite an epic fight back from Hamilton after serving his penalty.
It triggered celebrations in Italy where confidence in Ferrari has soared, but has left Mercedes with a problem to solve just three races into the 2017 season.
Vettel came in for new tires on lap 11, prompting Red Bulls Max Verstappen to pit on the next lap.
After claiming the first pole position of his career, Bottas said the fight for the championship was now a three-way battle, but the Finn will be desperately disappointed here after he finished a distant third.
A decisive moment in the race came a lap later when the safety vehicle was deployed for a collision at Turn 1 between Williams' Canadian rookie Lance Stroll and Toro Rosso's Carlos Sainz.
Hamilton was catching the German on every lap but ultimately ran out of time and finished nearly seven seconds behind.
"As a team, at least, we should have won but we didn't".
Valtteri Bottas admits being asked to allow Lewis Hamilton past him in the Bahrain Grand Prix was "a hard thing to accept" but the right call from Mercedes. Up ahead, Vettel managed to steadily increase the gap over Bottas, gaining a lead of around six seconds by the time the race had reached the halfway mark.
"Sebastian was in my blind spot so I didn't know where he was", Hamilton said.
Fernando Alonso was the last classified finisher in P14 for McLaren, pitting with three laps to go due to an engine failure.
Ferrari made a decision to bring Vettel into the pits for an early stop on lap 10.
"That is the interesting question that we need to analyse at the moment and I don't want to pre-empt what the consequences will be, or if there will be consequences".
Hamilton, now seven points adrift of Vettel, will return to the cockpit on Tuesday for the first of this week's two-day test in Bahrain.