Don't think it's a coincidence. Djokovic is like water eroding rock. Murray had been similar under Lendl. I think his recovery of the second set was helped by the protest breaking up the flow and allowing a break for Murray to cool down and refocus. I think as a continuous flow the pattern was going gradually away from him.
He did have Djokovic on the ropes a bit at that moment and early in the third. It looked like if he'd have been able to strictly sustain that and keep dictating he might have been able to drain the fight out of Nole's legs; but Djokovic was able to recover and turn it back. By the time he was 3 up in the 4th, it was clear Murray was a boxer who had no punches left.
Wonder how Murray evaluates that going forward, though I'm sure he'll be pleased in making the final. Remember him saying last year his plan with Mauresmo was to shift away from straining his body as much as he had been under Lendl, and focusing a bit more on a tennis based plan so he can take better care of it. His tennis has become a bit less cynical, though on evidence of that match, his endurance may have dropped to a lower level.
Also wonder if Nadal's health and game will recover in time for the French Open. It usually does, though it's been quite a while now that he hasn't looked like himself. He needs a proper run of matches, and he'll need his body to be up to that.
Could be a good year for Djokovic.