Zugzwang.
OK, one word is a bit short for an answer. :-) Still, I would win that one for White probably on blitz time. Note that Black has only one passer and your knight easily can put a cork to that. Thus, with still one minute on the clock:
- Play the N to f4 to kill Ph5.
- Black of course will object to that, playing Pe5 in time.
- Fine, then play the N to d3. The Pe5 now hangs.
- Either he goes to e4, now you can catch the Ph5 and easily be back in time, or Kf6, same result.
- Assume Black is lucky and manages to play Pe5, Pf4 without getting massacred. OK, same as before,
the N gangs up on Pf4, he must go to f3, the K can capture it.
- After that, back to the Ph5.
- Finally, queen the remaining Ph2 and mate.
A final warning. As Black I will try to let you play the N to f4, and when you capture h5, I have the K on g6, play e5 and YOU are in zugzwang. With one minute on the clock, I won't ponder if g4 still is won after f4 (it most surely is, but panic on the streets of London), but rather play the cool Nd3 instead of Nxh5 and we're at point 6 of the plan again.
Black can do zilch about this plan, White can execute it without much thinking.
To learn:
- No swapping of pawns if you are up a figure.
- No rushing in endgame. (As I commented above, bof's plan Ng5, Nxf7 also wins but do that only if you trust yourself, and Black can also foil it with Pf6.)
- No allowing of muddling the waters when you have a technical win.
- Make a decent plan.
- Make it in easily executable parts.