Kennedy then knocked an 0-1 fastball from Rivera (1-1) into shallow centerfield, scoring pinch runner Luis Rodriguez without a play at the plate.
"Sometimes in extra innings guys start to lose focus, but everybody stayed with it and the bullpen was great again and everybody had big at-bats," said Kennedy.
"I think that's my second hit off [Rivera] ever and my other one was just the same. It's not easy."
The Mariners have won 10 of their last 12 games, including the first two of this three-game series by one run each time.
The Yankees left runners in scoring position in the 10th and 11th innings and lost for the third time in five games.
"It's frustrating," New York manager Joe Girardi said. "We had leads in both of the games (in this series), that's the frustrating part, and we weren't able to hold them. We gave free baserunners and it hurt us."
David Pauley (4-0) picked up the win for Seattle after pitching the last two innings.
Hernandez yielded six hits and five walks while striking out four. Yankees starter Ivan Nova was chased during Seattle's three-run fourth and was charged with four runs on five hits and three walks in 3 2/3 innings.
Jeter had two hits and became the Yankees' all-time leader in stolen bases when he swiped second in the third inning. Jeter has 327 steals in pinstripes, breaking a first-place tie with Ricky Henderson.
Kennedy had three hits for Seattle, as did Gutierrez and Miguel Olivo, who was forced to leave the game after smacking his face in the dirt while sliding head first on an infield single in the 11th inning.
Cano belted a 3-2 pitch over the right field wall to lead off the second inning, giving the Yankees a 1-0 lead with his 10th homer of the season.
The Mariners scratched out a run in the bottom of the inning to tie the game, sparked by Cust's leadoff walk. He went to second base on Gutierrez's single and scored after Kennedy and Olivo grounded into back-to-back force outs.
The Yankees moved back in front on Teixeira's two-run homer to right field in the third inning, his 15th of the season, but the Mariners scored three in the fourth to take a 4-3 lead and chase Nova from the game.
Gutierrez singled leading off, moved to third on Kennedy's double and both runners scored on Olivo's ground-rule double, which hit off the warning track in right-center field and bounced over the wall. Olivo went to third on a wild pitch and scored on Brendan Ryan's single up the middle.
"He just had no command tonight," Girardi said of Nova.
Hernandez walked Jeter after getting a double play in the seventh, and it hurt him. Granderson followed with a triple off the wall in right field -- Ichiro Suzuki jumped at the warning track, but missed the ball -- and Jeter scored to tie the game at 4-4.
David Robertson struck out all three batters he faced in the bottom of the seventh. Hernandez was pulled to start the eighth and Aaron Laffey retired the two batters he faced before Jamey Wright got the final out for Seattle.
Neither team had a baserunner in the ninth, but the Yankees put runners at the corners with two outs in the 10th after Alex Rodriguez singled to left field and Cano roped a base hit to right. Brandon League got Russell Martin on a fly out to right to end the threat.
Kennedy grounded into a double play to end the bottom of the 10th and the Yankees stranded a runner at second in the 11th. Jack Wilson pinch ran for Olivo in the 11th, but the Mariners never got a runner past first.
This series started a nine-game road trip for the Yankees, who were just 1- for-9 with runners in scoring position Saturday, leaving nine men on base...The Mariners left 12 runners on base, but still improved to 2-0 on their 10-game homestand...Hernandez entered the game 4-0 in his last four starts against the Yankees.