user2042: The endgame is shown in diagram, and I have also submitted the moves from the actual game.
I want to know if any side can win, or is it really a draw. 
Support your claims with illustrative lines, please. Thank you.
[Title "Black to move"]
[StartFlipped "0"]
[fen "8/6p1/1pBnk1p1/pPp2pP1/P2P1P1P/2K5/8/8 b - - 0 1"]

1...c4 2.Bf3 Ke7 3.Be2 Ke6 4.Bxc4+ Nxc4+ 5.Kxc4 Kd6 6.d5 Ke7 7.Kd4 Kd6 8.Kc4 Ke7 9.Kd3 Kd7 10.Kd4 Kd6=

EDIT:
I must publicly apologize to user Ken Wei for unaccepting his answer. This is never a polite thing to do, and I will understand if there will be hard feelings. 
I thought that he checked the lines with the computer, but it doesn't seem so. 
User Matt pointed out refutation of user Ken Wei's answer. That is why I have unaccepted the answer, because I want to know the truth -> can any side win or is it a draw.
Therefore I urge future posters to prove their claims with concrete lines so we can avoid unpleasant scenarios.

user5835: In order to have a chance of winning, the white king has to be able to move to e5. By moving Kd6 if and only if white Kd4, black keeps the game a clear draw.

user7473: The final position is a draw, and is a case of opposition/corresponding squares. Black simply waits along c7-d7-e7, and plays Kd6 whenever white plays Kd4. (Although for future reference, you may notice that white can gain the opposition by sacrificing his pawn with d6, and meeting Kxd6 with Kd4, but in this case it doesn't win as the b6 pawn covers the entry point on c5; it would work if all the queenside pawns were shifted one rank towards the white side.)
It is crucial to recognise this idea from black's perspective, because it means that once the pawn on c4 is taken and the pieces are exchanged, white cannot win, so you need not calculate specific lines once you realise this: in particular, playing 3.Bd5 or 3.d5 for white makes no difference.
Hence white cannot win after 1...c4. To be specific for black: play c4, leave the knight on d6 and wait with your king. You need not worry about losing in lines where white plays h5, because after gxh5 Bxh5, the f5 pawn is protected by the knight (so Bg6 is not a threat), and e5 can be covered by the king in the pawn ending (so g6 does not win for white either, and in fact might even lose, but that argument is completely irrelevant).
Black certainly cannot win at any point: his knight is almost completely dominated by the white bishop.

user8066: OK:
1... c4 2. Bf3 Ke7 3. Bd5 Kd7 4. Bg8 Ke7 5.Bh7(!!) seems to win.
5... Kf7 6.d5 N somewhere and the King penetrates.
[Title "Black to move"]
[StartFlipped "0"]
[fen "8/6p1/1pBnk1p1/pPp2pP1/P2P1P1P/2K5/8/8 b - - 0 1"]

1... c4 2. Bg2! (2.Bf3 Ne4+! 3.Kxc4 (3.Kc2 Kd5-+) 3...Nd2+ 4.Kd3 Nxf3-+) 2... Ke7 3. Bd5 Kd7 4. Bg8 Ke7 5.Bh7! Kf7 6.d5+-


2042: <p>The endgame is shown in diagram, and I have also submitted the moves from the actual game.</p>

<p>I want to know if any side can win, or is it really a draw. </p>

<p><em>Support your claims with illustrative lines, please. Thank you.</em></p>

<pre><code>[Title "Black to move"]
[StartFlipped "0"]
[fen "8/6p1/1pBnk1p1/pPp2pP1/P2P1P1P/2K5/8/8 b - - 0 1"]

1...c4 2.Bf3 Ke7 3.Be2 Ke6 4.Bxc4+ Nxc4+ 5.Kxc4 Kd6 6.d5 Ke7 7.Kd4 Kd6 8.Kc4 Ke7 9.Kd3 Kd7 10.Kd4 Kd6=
</code></pre>

<h2>EDIT:</h2>

<p>I must publicly apologize to user <em>Ken Wei</em> for unaccepting his answer. This is never a polite thing to do, and I will understand if there will be hard feelings. </p>

<p>I thought that he checked the lines with the computer, but it doesn't seem so. </p>

<p>User <em>Matt</em> pointed out refutation of user <em>Ken Wei</em>'s answer. That is why I have unaccepted the answer, because I want to know the truth -> can any side win or is it a draw.</p>

<p>Therefore I urge future posters to prove their claims <strong>with concrete lines</strong> so we can avoid unpleasant scenarios.</p>
 5835: <p>In order to have a chance of winning, the white king has to be able to move to e5. By moving Kd6 if and only if white Kd4, black keeps the game a clear draw.</p>
 7473: <p>The final position is a draw, and is a case of opposition/corresponding squares. Black simply waits along c7-d7-e7, and plays Kd6 whenever white plays Kd4. (Although for future reference, you may notice that white can gain the opposition by sacrificing his pawn with d6, and meeting Kxd6 with Kd4, but in this case it doesn't win as the b6 pawn covers the entry point on c5; it would work if all the queenside pawns were shifted one rank towards the white side.)</p>

<p>It is crucial to recognise this idea from black's perspective, because it means that once the pawn on c4 is taken and the pieces are exchanged, white cannot win, so you need not calculate specific lines once you realise this: in particular, playing 3.Bd5 or 3.d5 for white makes no difference.</p>

<p>Hence white cannot win after 1...c4. To be specific for black: play c4, leave the knight on d6 and wait with your king. You need not worry about losing in lines where white plays h5, because after gxh5 Bxh5, the f5 pawn is protected by the knight (so Bg6 is not a threat), and e5 can be covered by the king in the pawn ending (so g6 does not win for white either, and in fact might even lose, but that argument is completely irrelevant).</p>

<p>Black certainly cannot win at any point: his knight is almost completely dominated by the white bishop.</p>
 8066: <p>OK:
1... c4 2. Bf3 Ke7 3. Bd5 Kd7 4. Bg8 Ke7 5.Bh7(!!) seems to win.</p>

<p>5... Kf7 6.d5 N somewhere and the King penetrates.</p>

<pre><code>[Title "Black to move"]
[StartFlipped "0"]
[fen "8/6p1/1pBnk1p1/pPp2pP1/P2P1P1P/2K5/8/8 b - - 0 1"]

1... c4 2. Bg2! (2.Bf3 Ne4+! 3.Kxc4 (3.Kc2 Kd5-+) 3...Nd2+ 4.Kd3 Nxf3-+) 2... Ke7 3. Bd5 Kd7 4. Bg8 Ke7 5.Bh7! Kf7 6.d5+-
</code></pre>
