Hamilton started from pole position but lost the lead on the first straight of the race as he was unable to defend Vettel’s overtake.
It means the Brit’s advantage at the top of the Drivers’ Championship has been cut to 17 points.
As the pair were fighting for control of the race, a major pile-up was happening in behind them.
On Turn One, Nico Hulkenberg broke late and crashed into the back of Fernando Alonso – sending him soaring over the top of Charles Leclerc. All three cars were forced to retire.
Fortunately for the Sauber driver, the Halo safety equipment saved him from suffering any serious injuries as the McLaren looped over his head.
Daniel Ricciardo also clipped Kimi Raikkonen on the same corner and the former retired on lap 30 after failing to make up his one-lap deficit to the rest of the pack.
Raikkonen also called his afternoon early after suffering substantial damage to the rear wing.
Max Verstappen took full advantage of the heavyweights dropping out to steam past both Force India’s, who had locked out the second-row, to move up to third and secure an impressive podium finish.
Hamilton never really got the chance to press Vettel as the Ferrari cruised to a comfortable victory.
But Hamilton’s team-mate Bottas raced extremely well to secure a fourth-placed finish after starting from the back of the grid.
The opening lap will go down in history as one of the most exciting of all time in Belgium.
Although Alonso is not looking at it like that just yet.
“It was bad on the start,” Fernando told Sky F1.
“I saw Hulkenberg in the mirrors with all four tyres locked and he was coming at very high speed. There is no way you can avoid that. He hit my car and then I went over Charles.
“Obviously he missed the braking point with high consequences. But on the positive side we are all ok, with Charles, with the Halo or whatever, it’s good news that all three of us are ok.
“It’s a good proof [for the halo]. We didn’t need any proof, but it’s a good thing. Something similar to 2012 at the start. When you miss so much the braking point and hit someone at that speed you need to think a little bit twice next time.”