There was early drama when the Toro Rosso cars of Frenchman Pierre Gasly and New Zealander Brendon Hartley almost collided.
The Formula 1 roadshow next moves on to Barcelona next, with Hamilton on top of the heap as the race for the championship title heats up.
Among the frontrunners Hamilton was the first driver to pit.
"That was an interesting race", a relieved Hartley said later, admitting he had some pace problems. "I am excited for the race, it is hard to overtake here, as it is anywhere around the world but we will give it everything we've got".
Vettel, who won the first two races of the season, leads Hamilton by nine points after three grands prix this year.
"The rest of the race I think there are only positives". Hulkenberg's race came to an end when he lost the rear of his vehicle at Turn 5 and hit the wall, while Sainz dropped down the order with an early pit stop but eventually went on to finish fifth following retirements further ahead.
"I would have loved to attack a bit more but let's be happy with a point on the board".
Vettel had comfortably led the race from pole position until his first pit stop on lap 30, after which Mercedes chose to leave Bottas out in the lead on worn tires to give him the chance to make a free pit stop in the event of a safety vehicle.
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Bottas retained the lead when he finally pitted under the safety auto, deployed after Ricciardo ploughed into the back of Verstappen as they braked from nearly 200mph 11 laps from the finish.
Vettel made a clean start. "I got caught out with the bump with the front locking, but I don't want to blame it on the bump with the front locking - in the end I am the captain on board".
With the Azerbaijan Grand Prix marking his first race win since the 2017 United States Grand Prix, Hamilton was asked if the fight for the championship is going to be an emotional rollercoaster for 2018.
"I don't think it was overly optimistic to jump down the inside". "This year, they've really outperformed us most of the time".
"That was close. We did the best job we could", said Hamilton.
Raikkonen, starting sixth, attempted to pass inside Ocon's Force India, but the Frenchman turned in and as the pair collided he crashed into the wall. I'll get through it, it's part of racing but at the moment it's very painful. "It just didn't work".
Both drivers received reprimands for their roles in the incident.
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Bottas had been left in the lead when first Hamilton, then Vettel, stopped for fresh tires.
During the race all went to the fact that Sebastian Vettel started on the pole and safely execute third victory of the season, but the scenario of the race changed dramatically after the collision the two pilots "Red bull".
"Without the safety vehicle it would have been easier for us - there is probably 47 laps of positive and maybe one turn without a positive note". That delayed the restart, and when it came Vettel charged down the inside of Bottas but couldn't slow enough to make the corner and went onto a runoff area. Hamilton now has 70 points in comparison to Vettel's 66.
Canadian Lance Stroll, third in Baku past year, will start 10th for Williams - the only team yet to score a point this season.
The safety vehicle came out following the contact between Verstappen and Ricciardo.
Sergei Sirotkin ran into the back of Perez, causing contact between several other cars. The Russian has been given a three-place grid penalty for the next event in Spain. Raikkonen needed to pit for a new nose and his chances of a podium finish appeared over. He was forced to retire as a result.
Vettel was fourth after failing to retake third spot from Perez. Vettel finished fourth, while Carlos Sainz in the Renault was promoted to fifth after the Red Bulls were out of contention.
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