Sexson hit a game-tying, two-run homer in the ninth inning and pinch-runner Jolbert Cabrera scored from first on a throwing error Wednesday, giving the Indians a 5-4 win over the Oakland Athletics.
The Indians, who trailed 4-0 before getting back-to-back homers in the eighth and three runs in the ninth, have won 11 of 12 and at 11-2 matched their best start since 1988.
"You always sit in bed at night and think of doing something like that," said Sexson. "It's neat."
Cleveland's last at-bat win was its second in nine home games this season and triggered a celebration inside and around Jacobs Field that made it feel more like October than April.
And with another dramatic win already this year, the 1999 Indians are drawing early comparisons to the '95 Tribe which won 17 times in its last at-bat. It's a new year, but it sure seems like old times to Indians fans.
"'95 was '95," said Kenny Lofton, who threw a runner out at the plate in the sixth. "This is '99."
So far this year, the Indians have done little wrong.
"These guys continue to show how good they are," Cleveland manager Mike Hargrove said.
Roberto Alomar and Manny Ramirez hit back-to-back homers in the eighth off Doug Jones after the Indians were blanked over the first 6 2/3 innings by Gil Heredia.
"Robbie's homer definitely fired us up," Sexson said. "It let everybody know that there were still two innings to play."
In the ninth, David Justice singled off Billy Taylor (0-1) and Sexson followed with his second homer, a 415-foot shot to right-center that sent the 299th straight home sellout crowd into a frenzy.
"I just felt happy, very happy, especially because I was 0-for-3, and a DH can't make a great play in the field to help his team," said Sexson. "So I'm mostly happy that we won the game, and I had a little to do with it."
Sandy Alomar singled and was replaced by Cabrera. Kenny Lofton then laid down a bunt in front of the plate, but after pouncing on the ball, catcher A.J. Hinch threw wide of first and the ball rolled all the way into the right-field corner.
By the time Cabrera rounded third, most of the Indians already were on their way to home plate to meet him. Cleveland has now won 61 games in its final at-bat since The Jake opened in 1994.
Steve Reed (1-0) pitched one inning for the win.
Ben Grieve hit a three-run homer and Tony Phillips had a solo shot for the A's, who have lost five of six on the road.
"It's an empty feeling," said Hinch who rushed his throw with the speedy Lofton going down the line. "You feel like you've been punched in the gut."
Heredia limited Cleveland to nine hits _ all singles. He struck out five and walked one.
"Heredia was tough," Sexson said. "He was getting ahead with some tough sliders."
Grieve hit his first homer of the season off Dwight Gooden in the sixth inning, and Phillips hit his fourth in the third.
Roberto Alomar went 3-for-4 with his first homer, Ramirez hit his fifth of the season and Sandy Alomar had three hits.
Gooden, the Indians' No. 5 starter, was making his second start of the season and first since April 10 in Minnesota, when he didn't get out of the first. He limited the A's to three hits in the first five innings, but a couple pitches just off the corners and one up cost him in the sixth.
Notes: Sexson's homer was the Indians' 500th regular-season homer at Jacobs Field. An Indians spokesman said with his BP shot, Sexson joined Mark McGwire as the only players to hit the scoreboard in left. McGwire hit a 485-footer off the board in April 1997 against Orel Hershiser. McGwire also hit it during batting practice before the All-Star game that year here. ... Cleveland's comeback kept the Indians starters unbeaten at 7-0, ... The Indians are 7-0 when both Alomar brothers get a hit. ... Gooden entered the game with a 67.50 ERA. He lowered it to 13.50.