"That's Yankee Stadium," Rivera said.
Cleveland had blown out New York 10-2 Thursday in the opener at the $1.5 billion palace and led 5-3 after five innings Friday.
"A lot of times it seems like the first one might be the most difficult to get," Jeter said.
Jeter, the Yankees captain, led the club to four World Series titles and six AL pennants across the street. That his home run gave the Yankees their first win in their new home seemed appropriate.
"If anyone's going to hit a game-winning home run for the first win at the new stadium, it's going to be Derek," Teixeira said.
Ceremonial bunting was gone, and the spectators in many of the priciest seats disappeared, too. Some of the tickets were unsold, and other spectators with tickets closest to the infield spent time inside the three areas serving them free food, leaving empty blue seats.
"We saw that. I don't think I've ever seen that at Yankee Stadium," said Jensen Lewis (1-1), who gave up Jeter's third home run of the season.
While the crowd was noisier than during Thursday's opener, it still seemed quieter than at the old ballpark. A better test will be when rival Boston arrives for a series next month.
"I thought it was louder today," said Cleveland's Mark DeRosa, whose check-swing strikeout ended the game. "Opening day is weird. It's not a representative game."
Jeter thought the crowd was noisy - at times.
"When we do something," he said. "If we give them something to cheer about."
The crowd of 45,101 was about 7,200 short of the listed capacity, but the Yankees said they didn't sell about 2,000 standing room tickets.
"We're very, very pleased because traditionally the game after opening day is soft, however, today's game significantly outpaced even the last year of the old stadium and 2007," he said.
Their second game in 2008 drew 48,544 to the old ballpark, which held about 57,000, and while the listed attendance for the second game in 2007 was 52,096, the Yankees said the turnstile count that day was about 41,000.
Fans Friday saw all five of New York's home runs go to right field. Cano become the first player to reach the new stadium's second deck and Teixeira, playing a day following a cortisone injection to his sore left wrist, homered off the facing of the second deck.
"I'm glad it's finally feeling better. I could take some semi-normal swings today," Teixeira said.
New York was so successful at the old stadium, which still stands, that its all-time record there never dipped more than a game below .500 and that was only in 1923, when the stadium opened. For a while, it appeared the Yankees might drop to 0-2 at their new place.
Given a 3-2 lead after four, starter Joba Chamberlain walked his leadoff batter in the fifth, and Cleveland went ahead on DeRosa's run-scoring single, Victor Martinez's sacrifice fly and Ryan Garko's RBI double off the manual scoreboard in left.
Cano homered in the sixth against Zach Jackson, who relieved starter Anthony Reyes. Then in the seventh, Vinnie Chulk walked Damon leading off and threw Teixeira's grounder wide of first, allowing Damon to come home on the error.