It is extremely difficult to say for certain. I can easily contradict any answer I give, but I will try to give as good an answer as I am able.
To begin with, Windu is an extremely spectacular jedi, being one of only two to carry the high jedi general rank, and inventing his own brilliant style. My assumption straight off is that Windu was the only one able to resist Sidious's force shout, being quicker and perhaps more skilled than his companions, thus he was able to stay alive longer.
The area of which the duel takes place also seemed to be in Windu's favor, because Sidious gives me the impression of being more of a force user. I do remember that he did well to keep distance from Yoda in their duel if he could, and he only gained the upper hand when he did so.
So really, a part of me thinks Windu was able to overcome Sidious here, because of where his strengths come into play and where they are coming into play at. But then I can easily argue that it fits together all too perfectly. Sidiou's plan was obviously for some sort of fight to happen there. He knew that Anakin wouldn't so easily convert merely because he revealed himself to him at a time of distress. No, he had to fit the key perfectly.
So I think he did mean for the duel to happen. I also think that, while he may have wanted Anakin to come in at a point where Sidious was still locked in combat, he didn't particularly want to go so far.
Then I come to ask myself, wouldn't he be wiser than to throw a volley off lightning at Windu, who still has his saber up? Did he deliberately do this, to put himself on the edge and force Anakin into choosing right then and there? Or was it just a moment of despiration?
In the end, I'd have to say that, given the advantages, Windu did truly overcome Sidious, who did mean for everything to happen, but maybe not exactly how they did. But that's just my guess, and I know a lot of people out there are able to do a much better job at it than I did. Just figured I'd share.
"Neither dark nor light, but both all the same.
Neither hero nor villain, but both all the same.
Neither balanced nor chaotic, but both all the same.
Neither alive nor dead, but both all the same."