How would he avoid a checkmate the best way?

Well, this was a match against a very "move wasteful" opponent, but I would like to see if you guys could help me analyse this..

[Event "ChessCube Game"]
[Site "www.chesscube.com"]
[Date "2012.10.06"]
[Round "-"]
[White "newba@chesscube.com"]
[Black "xmiec_@chesscube.com"]
[Result "1-0"]
[WhiteElo "1843"]
[BlackElo "1822"]
[Time "05:06:49"]
[TimeControl "300"]

1. e4 d5 2. exd5 Qxd5 3. Nc3 Qe5+ 4. Nge2 Nc6 5. f4 Qh5 6. Ng3 Qg6 7. Bb5 a6 8. Bxc6+ Qxc6 9. O-O Nf6 10. d4 Bg4 11. Qd3 O-O-O 12. Be3 h5 13. h3 g6 14. hxg4 hxg4 15. Rad1 e6 16. Nge4 Nd5 17. Nxd5 Qxd5 18. Nf6 Qa5 19. Qb3 Bg7 20. Nxg4 Rh4 21. Ne5 Rf8 22. Nf3 Rg4 23. d5 Rh8 24. dxe6 Qh5 25. Kf2 fxe6 26. Qxe6+ Kb8 27. Rh1 Qf5 28. Qxf5 gxf5 29. Rxh8+ Bxh8 30. Rd8# 1-0

Do you think there was any sort of way for black to prevent mate? I mean, the game was already lost alright, but in how many moves you think it'd be forced mate after 27. Rh1? It could do queen and rook sacs on h4, perhaps, but then, how could I mate it the quickest way? I'd have a huge material advantage, and open fields, but that rook on h8 was the main reason for my topic, since it's protecting the h file solely and undiscordely.

I thought that after the trades at h5 I could do Qd5 or Qd7, to double up and strike at the end, but what if after that black just went with Rc8?

Their king is very nice at the corner, while mine is a bit messed up. I'd surely lose that game if the guy wouldn't have made so many waste moves, don't you think?
Note that trading the queen for two rooks would be possible for black, but would also lose a rook after Qxg4 and, well, perhaps leave in a slower position.

I know it's an amateur game, but that position got me a bit.
Cheers!

Good day,

First of all I must say that your move 28 QxQf5 is totally unnecessary. Since you already have 28 RxRh8+ Qf8 29 Rh8xQf8+ BxRf8 30 Qe8# or Rd8#

Now in your game if you do 28 QxQf5 then it is not g6xQf5 instead it is Rg2 or Rc2 and white needs to do more moves to mate although black is lost.

But then again if 27 Qf5 there are the moves I have said to mate in 3. Which makes 27... Qf5 not a good move to avoid fast mate.

I think that the key move is 23... Rh8 it is e6xd5 or any other move. Since after 27 Rh1 black seems quite hopeless. 27... QxRh1 28 RxQh1 Rd1 29 QxRg4 and white wins although not really fast.

Regards Xabier.