According to ELIAS

Dusty Baker‘s first win like this one

The Nationals defeated the Twins in 16 innings on yesterday after trailing in the ninth and 15th innings. Dusty Baker has won 1,685 games as a major-league manager, but this was his first in which his team trailed in the ninth inning and again in extra innings.

The last time that a major-league team tied a game with a bottom-of-the-ninth home run and won it in the 15th-inning or later with another homer came on May 25, 2008 when the Padres defeated the Reds, 12-9, in 18 innings. Scott Hairston hit a game-tying ninth-inning home run and Adrian Gonzalez had a walk-off home run off of Edinson Volquez.