No, your opponent can't do that.
If you have connection issues when you're losing, it's not as memorable. Connection issues when you're hoping to win the game has a much larger impact psychologically... so it seems like this only happens "when you play a winning move" but it probably happens at random, and having a nice position is different from playing a winning move. For example if you had disconnected 1 move earlier would you have felt the same way? Since you were winning, probably you would feel the same way.
What about 2-5 moves earlier? Again, if your position was good, you'd probably feel the same way. etc. So it doesn't happen when you play a winning move. It's just that losing from a favorable position due to disconnect is very frustrating.
I have experienced not a few occasions when I get disconnected from Chess.com. Funny thing is, it usually happens when I made a winning move and just after, I get disconnected. Is there a way that my opponent is deliberately doing this? can they do this?