Webber held the lead for most of the race, fending off a five-car train of pursuers amid drizzle on slick tyres in the final laps.
The Australian said wondering when it might rain made all pit strategies a gamble, but he was able to fend off main rival Nico Rosberg despite the Mercedes pitting for fresh tyres earlier.
"I'm feeling incredible. It was a very interesting race," said Webber. "It was reasonably straightforward at the start, getting the gap on the super softs and just managing with Nico. We had a bit of a gap over the rest so both of us were getting away and trying to get into a reasonable gap.
"The weather was threatening around that pitstop window - we didn't know whether to go a bit longer and put on a set of inters. Nico went for the undercut so a few people had to react to his chess move."
Webber's team-mate Sebastian Vettel then became a threat for victory as he ran long on soft tyres and pulled away while the erstwhile leaders struggled for tyre temperature on the new softs they had just taken on at their stops. Ultimately Webber got up to speed and Vettel could only get fourth place.
"The next stage of the race was very strange as it was hard to get the soft tyre warmed up," said Webber. "Seb had his [tyres] in and it wasn't really wearing down that much and he was coming back into the picture with his strategy.
"I thought it was getting interesting and didn't want Seb to get the magic 20 seconds so he could do the stop and get the victory, that wasn't part of the plan."
The rain finally came with eight laps to go, and Webber had to hang on with Rosberg, Fernando Alonso, Vettel, Lewis Hamilton and Felipe Massa right behind him as they coped with both a slippery surface and traffic.
"Fernando said in the car coming across here that there were times when he was praying for rain, then when it started he was like 'no, no, no'," Webber joked.
"I think it was like that for all of us except me because for the first guy there it is always tricky."