In Game 5 of Karpov vs. Korchnoi for the World Championship in 1978, Korchnoi missed a forced mate when he played Be4+ instead of Bf7+ on move 55. The game ended as a lengthy draw.
The match was being played as first to 6 wins with draws not counting, and neither player had won a game out of the first four. The match ended as a 6-5 win for Karpov in 32 games after Korchnoi nearly came back from the 5-2 deficit he faced after 27 games. Korchnoi won games 28, 29, and 31, and drew game 30, tying the match at 5-5 before Karpov won Game 32 to retain his title. Had Korchnoi won Game 5 and every following game played out the same, he would only have been down 5-3 following game 27 and the following three victories would have won Korchnoi the match in 31 games.
This was a dramatic match that had bizarre allegations of cheating, as Guest_On_StackExchange mentioned in the comments to the original post. Additionally, this match had a similar dynamic to the match friscodelrosario mentioned, with Korchnoi being a Soviet defector challenging a Soviet champion. Korchnoi winning could have fascinating political/propaganda impacts on your alternate timeline.
Details of the forced win:
55.. Kc6 (forced)
56.. Kb5 or Kb7
57.. Ka4 (forced)
Black can play Nd7, Kc8, Kc6, Ka6, or Ka8, but all are lost
If Nd7 then Qxd7+ and Ka8 Qc8# or Ka6 Bc4+ b5 Qxb5#
If Kc8 then Qc7#
If Kc6 then Qc7+ Kb5 Bc4+ Ka4 Qxa7#
If Ka6 then Bc4+ b5 Qd6+ Kb7 Qb8+ and Ka6 Bxb5# or Kc6 Qc7#
If Ka8 then Qd8+ Kb7 Qc7+ and Ka8 Qb8# or Ka6 Bc4+ b5 Qc6#