Vettel’s drivers championship rival, Lewis Hamilton, could only finish back in seventh in the other Mercedes having started in 13th position after a nightmare qualifying session Saturday.
Having started second on the grid behind Raikkonen, Vettel had to wait for his moment to hit the front.
He eventually took the lead after Raikkonen pitted from the the front on lap 35.
That allowed Vettel who had been closely following his teammate to put his foot down and make the most of the open road in front of him before pitting four laps later.
As the German driver returned to the track, he did so just in front of the fast approaching Raikkonen who was looking to reclaim first spot.
With the lead now locked in, Vettel was able to keep his nose in front on the notoriously narrow Monaco track and negotiate his way to the checkered flag.
“It was a very intense race. I was hoping at the start to have a bit of a better launch. Kimi had a really good start but I had to be patient.” Vettel said after race.
“We couldn’t plan much but the plan was to pull away and as soon as the gap opened I took it. I was surprised myself,” the four-time world champion added.
Having been fastest in practice and qualifying, Raikkonen was visibly disappointed at missing out on what seemed like a golden opportunity to win his first race since 2014.
“It’s still second place, but it doesn’t feel awful good,” Raikkonen said. “It is how it goes sometimes but we go to the next race.”
Elsewhere on the track Sunday, the points positions were closed out by Romain Grosjean for Haas, Williams’ Felipe Massa and Kevin Magnussen in the second Haas.
Only 13 cars finished after a number of bumps and crashes over the course of the race.
One of the most dramatic was when McLaren’s Jenson Button hit the side of Pascal Wehrlein’s Sauber, flipping it over into a collision with a side barrier.
Four-time world champion Vettel now heads the drivers championship standings by 25 points from Hamilton.
Valtteri Bottas remains in third followed by Kimi Raikkonen and Daniel Ricciardo.
Ferrari’s one-two in Monaco ensures they lead the constructor’s standings.