The Sox take the first game of the three-game series with relief pitcher Garrett Whitlock earning his fifth win of the season.
A controversial 10th inning began after Anthony Volpe was called out at third during a bang-bang play that emptied the bases for the Red Sox thanks to a great heads-up throw from Narvaez, the former Yankees catcher.
However, Yankees manager Aaron Boone was tossed from the game shortly after when it was decided that a line drive down the right field line hit by second baseman DJ LeMahieu was ruled foul.
LeMahieu himself would then be tossed from the game after saying something to the first base umpire following a groundout to end the top half of the inning.
Boston Red Sox starting pitcher Garrett Crochet lasted 8.1 innings, giving up one run on four hits while striking out seven, three of which came against New York Yankees star outfielder Aaron Judge.
But the Yankees slugger got his revenge in the ninth inning, launching his 26th home run of the season over the Green Monster to tie it all up at one apiece.
Judge is now tied with Seattle Mariners catcher Cal Raleigh for the most homers in baseball.
Yankees relief pitcher Tim Hill received the loss, his second of the year. Starting pitcher Ryan Yarbrough went 4.2 innings, giving up one run on four hits while walking three and striking out three.