Is there a forced mate/ winning advantage? Recently I played a game in a High School league match as the top board. I played f4 followed by d5 (very standard). I played passively and waited out his attack and soon gained the momentum. At around the 25th move we progressed to this situation:

 [FEN "r5k1/p1q5/5rp1/2p1Np2/1p1n1P2/1P1PR3/P1P2Q2/1K2R3 w - - 0 1"]
 [Title "White to Move"]


It was my move and I saw mate in 3 with Qh4/Rh1/Qh8++.

So I played Qh4 attacking his rook and impending mate. He responded Qg7 which I feel was a strong defense.

That's when I saw my winning move from this position: 

 [FEN "r5k1/p5q1/5rp1/2p1Np2/1p1n1P1Q/1P1PR3/P1P5/1K2R3 w - - 2 2"]
 [Title "White to Move"]


Nd7!

How does he respond without going down the exchange or significant material?

If - QxN 

QxR down the exchange and threatening to take more.

He plays Rd6?

[FEN "r5k1/p2N2q1/3r2p1/2p2p2/1p1n1P1Q/1P1PR3/P1P5/1K2R3 w - - 4 3"]
[Title "White to Move"]


Re8+ now wins, right? There's a mate there for sure, but can he escape without losing his queen? If not the game?



     [FEN "r3R1k1/p2N2q1/3r2p1/2p2p2/1p1n1P1Q/1P1P4/P1P5/1K2R3 b - - 5 3"]
     [StartFlipped "0"]
     [Title "Black to Move"]



black resigns.

EDIT:
After some analyizing I think after Nd7 Black has lost. I cant see any possible escape from an actual Mate. please correct me if I am wrong.
Congratulations on a fine win. I see you have dominated the center with your knight which is backed up by doubled rooks on an open file.  Your king is in a safe position, compared to black's drafty King position. Black's queen is passive though not poorly placed. One of black's rooks is still in the box and is undefended.  It's vulnerable.  The other rook is also undefended and passive. But at least it is offering a feeble defense.

If you dilly-dallied, Black could move his knight to the awesome c3 square. So I am glad you did not do that. Also, if the pieces suddenly disappeared from the board, he would have a passed pawn on the f-file which could be fatal for you.

This position proves the adage, "If you find a good move, wait, and find a better move."  White wins with Qh4.  I'm sure you can win this game by force but I can't find a mate. It's amazing how resilient even crummy positions can be, if the losing player is willing to play until the bitter end.

This statement set off my danger alarm:


  QxR down the exchange and threatening to take more.


Being up the exchange is not a clear-cut win. You need to see the 'more' before assuming you're going to get the full point.

Qh4 is spot-on in that it forwards an agenda (exploit the drafty house) while hitting the lose rook. What's not to like?  But what I think you have missed here is the wretched state of the g6 pawn.  What if you double up on it with Qg2.  Now you're threatening to denude the king even more, while hitting the lose liability, oops I mean rook, on a8. Because Black's rooks are lose, you can move with tempo. It's like getting free moves.



[FEN "r5k1/p1q5/5rp1/2p1Np2/1p1n1P2/1P1PR3/P1P2Q2/1K2R3 w - - 0 1"]

1. Qg2 Raf8 2. Nxg6 (2... a6?? 3.Ne7+ Kf7 4.Qd5+ looks_strong) Rxg6 3. Qxg6+ Qg7 4.Qd6



The a6 move is a throw-away to show what can happen if Black plays poorly. It's what's coming if he does not take evasive action.

The main line sees you getting an exchange and a pawn. Super easy, too, and offers Black nothing in return.  Now your queen dominates black's undefended queenside. The c5 pawn will likely fall, leaving the Knight trapped. If he saves the Knight, you probably get the b4 pawn if you want it.  NOW if the pieces drop off, you have connected passed pawns.

Black's king will never be safe with white's queen and rooks on the board. This means he must always defend against fast checkmates and getting pieces pinned against the king. He's going to be down material and defensive. Further, I don't see how black holds the c5 pawn and he's in danger of losing the knight which is hemmed in.

Edit - I like to run positions in Stockfish (a chess engine.)  I let this one run. 20 minutes into its analysis, it switched black's first response from Raf8 to Nb5.  That is, it advocates that black simply drop the rook on a8. 1. Qg2 Nb5 2. Qxa8. wow. It rates the initial position as a crushing win for white. What is important to realize is that the moves are there if you're clever enough to find them.