Jalen Brunson hit a go-ahead free throw with 9.5 seconds left after a crucial turnover by Victor Wembanyama moments earlier, then Wembanyama missed a jumper at the end of the game to give New York the win on Friday night.
The series will move to New York for the next, and potentially final, two games after the Knicks took control in Wembanyama's backyard.
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"New York City showed up," Karl-Anthony Towns said. "The fans showed up. The energy showed up. And we found a way to get it done."
Towns had 21 points and 13 rebounds, while Brunson and Mikal Bridges each scored 20 for the Knicks.
They have won 13 straight games, the second-longest streak by any team in NBA playoff history.
The Knicks are also now just the third team to win the first two games of a finals on the road, joining Michael Jordan and the 1993 Chicago Bulls, and Hakeem Olajuwon and the 1995 Houston Rockets.
Both of those teams won championships, the Bulls needing six games to oust the Phoenix Suns, the Rockets going home after winning those first two games in Orlando and sweeping the Magic. The Knicks, seeking their first championship since 1973, are in position to join them.
"We can't change the past," Wembanyama said, "We're already thinking about Game 3."
The Spurs were down 14 midway through the fourth and came all the way back - scoring the next 14 points to tie the game.
Wembanyama's three-point play with 57 seconds left gave the Spurs their first lead in nearly two full quarters, putting San Antonio up 104-102.
But the Knicks got the last three points, with Brunson - the hero of Game 1 for the Knicks - getting them all.
Brunson scored on the next possession, just his seventh basket in 24 shots on the night, and the game was tied.
Wembanyama, who scored 29, missed a long jumper, OG Anunoby got the rebound for New York with 30 seconds left, the Knicks called time and the stage was set.
The Spurs got a stop, but Wembanyama threw the ball away. Brunson got fouled, the Knicks had the lead back and called time with 7.5 seconds remaining.
Fox took the inbound pass, then set up Wembanyama for a jumper that would have won it. The shot bounced off the rim, and it was over.
Game 1
Knicks 105-95 Spurs
Game 2
Knicks 105-104 Spurs
Game 3
June 9 - Spurs @ Knicks - 1.30am
Game 4
June 11 - Spurs @ Knicks - 1.30am
Game 5
June 14 - Knicks @ Spurs - 1.30am
Game 6
June 17 - Spurs @ Knicks - 1.30am
Game 7
June 20 - Knicks @ Spurs - 1.30am
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