Ferrari's Fernando Alonso and McLaren's Jenson Button, who briefly led the race, had closed in on Vettel but a late safety car helped the German.
Alonso finished second for the first time in 2011, with Button third and Red Bull's Mark Webber fourth.
Lewis Hamilton became embroiled in a row over critical comments about stewards after finishing sixth.
The Englishman was called before officials for two separate incidents and, asked why he had been to see stewards five times in six races this year, he said, apparently in jest: "Maybe it's because I'm black. That's what Ali G says."
The race was poised for a thrilling finish as Vettel, Alonso and Button were covered by less than a second and chasing each other hard.
But with just seven laps to go, Renault's Vitaly Petrov got caught in a pile-up and plunged his Renault into the barriers at the Swimming Pool.
After complaining of pain in his left ankle the Russian was taken to hospital for a body scan, but Renault subsequently released a statement confirming there was no swelling or broken bone.
The reappearance of the safety car released the pressure on Vettel, and when the race resumed 20 minutes later with the three leaders all having changed their tyres, Vettel comfortably held off Alonso and Button to add the Monaco title to his growing collection.
Red Bull team principal Christian Horner said it had been particularly pleasing to win after the team had experienced a series of unexpected problems during the race.
"We had problems at Sebastian's first stop, we had radio issues and didn't get the tyres on that we wanted, so we had to change our strategy," said Horner.
"The main thing was that we didn't panic. We tried something a bit different, which was very aggressive, but Seb was making it work - that was what won him the race today.
"He was pretty confident, kept talking to his engineers, focusing on areas he could be quick."
BBC F1 chief analyst Eddie Jordan praised Vettel.
"Since he became world champion he has been supreme," said Jordan.
"He is always in the right place - but he also had luck on his side."
Monaco is regarded as the most challenging circuit on the calendar because the narrow, twisting streets push the drivers to the limit.
And Vettel had taken his first pole in Monte Carlo during a qualifying session which had been overshadowed by Sergio Perez's heavy crash which kept him out of the race.
Button, who started alongside Vettel on the front row, tried to play a decisive card in the race when he triggered the pit stops on lap 15.
Vettel had no choice but to respond and came in for his first stop on the following lap, but his crew of mechanics in the Red Bull garage did not have the tyres ready. The resulting delay saw Vettel return to the track in second place.
With a clear track ahead of him, Button quickly built a lead over the world champion.
But while a clever strategy call helped McLaren and Hamilton win in China, this time their attempt to out-think Red Bull backfired.
Button was on a three-stop strategy and when he came in for a second time Vettel regained the lead, and Button dropped to third after his final stop.
The Englishman refused to blame his team's strategy for failing to deliver him his first win of the season.
"We had to take the risk and go for more stops so we shouldn't be upset with what we did," said Button.
"The team did a great job this weekend and I was happy with our strategy. We had to try to do something different to beat Vettel, it was working but it didn't work in the end."
Alonso had muscled his way past Webber and up to third with a typically aggressive start and the Spaniard gained another place thanks to a two-stop strategy.
Vettel looked in real danger as his one-stop strategy meant he had to nurse his tyres for more than 60 laps.
But the restart after the second safety car meant the three leading cars were able to change their tyres and Vettel comfortably cruised to the line.
Alonso said: "Seven days ago we were two minutes behind the leaders and now we are fighting for victory.
"The car is identical to Barcelona so [this result] is just related to Monaco's unique circuit.
"It is also true that the car is working well on the supersoft tyres. They will be available for the next two races so hopefully we can repeat this performance."
Hamilton had a rollercoaster of an afternoon and was constantly in the thick of the action.
After a tussle with Michael Schumacher's Mercedes, Hamilton received a drive-through penalty after he bumped Massa in a three-way battle with Webber at the hairpin.
It's not too late [to win the world championship] but it's not looking great The Englishman was ninth with seven laps to go, before Jaime Alguersuari's Toro Rosso rode over his McLaren, breaking the rear wing.
The team repaired Hamilton's car before the restart but Hamilton was soon back in trouble with the stewards when he collided with Pastor Maldonado's Williams at Sainte Devote - an incident for which he was subsequently penalised with the addition of 20 seconds to his finishing time, although the punishment which left his finishing position unchanged.
The battle at the hairpin also had repercussions for Massa as Hamilton hustled him again in the tunnel, and as the McLaren sailed safely through, Massa lost control on the tyre debris in the tunnel and hit the barriers.
It is the second race in a row that Massa has retired.
"I was quite a lot quicker than Massa, I went up the inside - and he turned in," said Hamilton in a fiery interview after the race.
"I get the penalty [though], which is usual. He held me up in qualification, I got the penalty. He turned in to me, I got the penalty.
"But you get done trying to put on a show, trying to make a move. Fair play, if I feel I've gone too late I'd hold my hand up to admit I've caused an incident.
"It's not too late [to win the world championship] but it's not looking great."
Schumacher, a five time Monaco winner, conjured up memories of former glories in the opening stages of the race when he brilliantly passed Hamilton at the hairpin.
"That's something I thought you'd never see," said BBC F1 co-commentator David Coulthard. "Hamilton, one of the best racers in the world, caught napping by Schumacher - an inspired move."
But Schumacher fell back as his tyres quickly deteriorated, a problem with which his Mercedes team-mate Nico Rosberg also struggled, before Schumacher eventually retired with a fire in his airbox. Rosberg went on to finish 11th.
There was some much-needed positive news for Sauber as Kamui Kobayashi finished fifth on a one-stop strategy. It was very nearly fourth, the Japanese driver only being passed by the charging Webber on the penultimate lap.
Kobayashi called it a "great achievement" after a difficult weekend with his team-mate Perez still recovering in hospital after a qualifying crash which left him with concussion and a bruised thigh.
Adrian Sutil collected sixth for Force India, but his team-mate Paul di Resta was 15th after receiving a drive-through penalty for a mis-timed pass on Alguersuari.
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