"He just keeps thrilling us all, in a sense," Girardi said.
Teixeira lifted Montero's second pitch of the sixth to right-center for his eighth home run and seventh in his last 15 games.
Jeter's infield single, a dribbler that barely traveled 20 feet out in front of home plate, scored Brett Gardner in the seventh.
"I knew that we were in a little funk, losing four in a row, and I also knew that we hadn't won a Subway Series in a while. So yes, I did want to go out there and try to get a win for us," Tanaka said.
NOTES: Yankees RF Carlos Beltran (right elbow) was still unavailable but reserve outfielder Ichiro Suzuki (back) was feeling better, Girardi said. ... Sabathia had his sore right knee drained and the Yankees hope he can return as soon as his 15-day stint on the disabled list is up, Girardi said. Sabathia was examined by Dr. James Andrews and is receiving treatment. ... The Mets plan to commemorate Jeter's final regular-season Subway Series game Thursday.