Neo made a Telnet connection to the Source, temporarily allowing him to override the Sentinels and fry them. This, as MasterWizard pointed out, was too much for him to take the first time, as he didn't know this power existed, so he went into a coma. However, Neo was ready for it, and understood it, the next time, after he was blinded, and could see the coding of the machines. I am assuming you have seen Revolutions, but judging from your question i would say that you haven't.
The power of the One extends out of this world (the Matrix) right back to where it came from..the Source.
AI... a singular consciousness that spawned an entire race of machines. I don't know which came first programs or machines but what I do know is that it was from the machine mainframe that all them where created and made.
The source of Neo's powers is the source. That's what Neo say when he was blind. So the matrix and the machines are all connected to the Source, that's how can control both.
You could also speculate that the reason for this is that Neo is infact a computer program in a human body like Bane. Your five predeccessors were by DESIGN based on a similar predication, a contingent affirmation that was meant to create a profound attachment to the rest of your species facillitating the function of the One.
It's even possible that Neo wasn't looking for Morpheus or the answer to what the matrix was at all but looking for or to return to the Source, where the path of the One ends.
But that's a discussion for another day.