With Webber on pole and Vettel starting from ninth on the grid, the team were forced to adopt different strategies for their two drivers. Webber grabbed the eighth win of his Formula One career, and second around Monaco, with Vettel climbing to fourth.
It has been suggested, however, that with drizzle falling over the closing laps Webber backed up the field to allow the German a crack at second-placed Nico Rosberg and Fernando Alonso, who finished third.
"That is absolute rubbish," said Webber. "You just cannot be that fancy around Monaco.
"Seb ran out of tyres and he had to pit because the rest of us started to go quicker, but if they'd kept going, he would have been pushing for the win.
"If we had been trying anything on, I could have been even cuter. I cleared Seb [in the pit stop] by quite a lot. If I'd wanted to slide him in among other people, I could have slowed down and it would have been even better for the team, but it just wasn't part of the plan. The problem with trying to do that would be that you're exposing yourself to even more pressure from the guys behind – Nico and Fernando in this case. And then the boys in the pits might mess up Seb's stop and it would all be for nothing."
Lewis Hamilton is hoping an error-free weekend will finally give him a win, in Canada next weekend.
The opening six grands prix have produced six different winners, but the former world champion has not been one of them.
"I just hope we get some updates to edge us closer to the others, and then I hope we have a weekend where we have nothing go wrong, because the other guys are doing a fantastic job," said Hamilton.
Asked if he could believe he has yet to win a race yet this year, Hamilton replied: "I can, yeah. For what reason, though, I really don't know. We haven't had a grand prix weekend where something hasn't gone wrong.
"The start of the race in Monaco was the beginning of things, and then I don't know what else happened after that. My pit stop didn't feel very quick, but generally we weren't quick throughout the race, which is strange.
"It really wasn't great when we lost positions to Fernando, and then to the Red Bull in such a short period of time, I don't know – half a second or something.
"But we still got points, even though it wasn't the best of weekends."