I'm sure we've all had games where the "winning" opponent overlooked a swindle that brought us back into the game. I think the more interesting stories would be those where a long-range plan ended up saving the position. An opponent who realizes what you are doing would have plenty of time to counter the plan, but a subtle plan has a chance of succeeding against opponents that would not fall for a two-move swindle.
In the late '80s I had a game against another expert (40/90, 30/60) where I reversed two moves and lost a piece for a pawn in the opening. I was able to pick up another pawn and go into a K+bcgh(Pawns) vs. K+B+cg(Pawns) ending. His K was on the K-side and his B was restricted behind my K and bc on the Q-side (where I had exchanged my last piece - the B could not be captured but it was unable to move much). I sac'd my gh for his g (otherwise I would have a protected passer and it would be an easy draw with his K tied down there and his B unable to escape) and released his B during the process of sac'ing my bc for his c. That left my K drawing his K+B.
A year or so later against another expert I found myself forced to lose an exchange, but was able to wrangle two pawns for it. I pushed those pawns down the center of the board and forced him to trade a piece for each. Entering the endgame with three pieces for the rook made for a fairly easy win.
Way back when I was only a B-player the club had an A-player, expert and master that would analyse games to the point where the win was clear. Just to make sure though, they would then ask me if there was any way to save the "losing" side. I often came up with defensive plans that were unanticipated, difficult to overcome, and sometimes held the draw.
I've had a number of games where it was obvious that an attack would eventually break through against me. I've responded with quietly prepared counterattacks (that could have been stopped if prevented before launching them) and have ended up winning some of those games.
One time I ended up escaping in a position that I initially analyzed as one I was winning all the way. I sac'd a Q for a R+P with the expectation that my opponent would have his Q trapped and have to sac' back a Q+P for an R (leaving me 2P up). After sac'ing I discovered that I really needed two more moves of preparation before making the sac' (a little late to notice that). However, he thought I had to be preparing to attack his K and made two defensive moves there that allowed me to finish the web around his Q. Those extra 2 pawns won it in the ending.