Both men had opted to stay on slicks during the first shower at around mid-distance, with Hamilton in the lead and Rosberg bottled up behind the two Williams in fourth.
As conditions worsened, Rosberg picked off both Valtteri Bottas and Felipe Massa, and began rapidly closing on Hamilton. At that stage the German was confident slicks remained the faster tyre, and therefore opted to stay out when Hamilton pitted on lap 43 - a decision that would ultimately cost him a shot at victory, as he struggled for grip and surrendered around 10 seconds before being able to pit the next time around.
"I was very thankful when the rain came," Rosberg said. "I felt great. I was able to attack and pass both Williams, and close in on Lewis a lot.
"I was hoping it would stay more or less like that, and I thought I could attack Lewis at some point - and then Lewis boxed. I was pretty sure it was the wrong call because it was still touch-and-go at that time. So I was actually quite happy that he boxed.
"But it was the right call in the end. It started raining more on that lap, so that was it. I had to take that chance [of staying out one lap] because just following Lewis into the box is definite a lose for me, so I might as well take the chance, stay out and do one lap more at least. It didn't work out."
Hamilton, meanwhile, said he had seen more rain arriving, and had therefore made the call to stop.
"The rain came and I think I just lost temperature in my front tyres," he explained. "It's always trickier for the guy who's out in the lead because you're the first one to get to it and it's questionable how much risk you take.
"But for the first time I think in my whole Formula One career, I made the perfectly right choice in coming in now [on lap 43]. I could see the rain coming more and I've never had that before, so I feel extremely happy about that."
The result enabled Hamilton to stretch his advantage over Rosberg atop the championship standings back to 17 points.