The Atlanta Braves were leading 2-1, but the New York Mets had the bases loaded with two outs and Glavine at the plate.
Smoltz got Glavine out on a pop to third and the Braves went on to a 5-3 win Saturday, handing the Mets their first loss of the season.
"I honestly didn't want to face him in that situation. That's for the rest of your life smack talk right there," said Smoltz, who exchanged words with Glavine following the out, but did not reveal what he said.
It was the second time Smoltz had faced Glavine after 15 years as teammates and golf buddies. The Atlanta right-hander also won on July 15, 2005, but wasn't ready to give himself bragging rights.
"No. It's not necessary. I think bragging rights depend on who wins the division and goes to the World Series," he said.
Smoltz (1-0) went six innings and allowed two runs, seven hits, walked four and struck out four. Bob Wickman got Shawn Green to line out to first with runners on second and third to pick up his second save.
Glavine (1-1) pitched 5 1-3 innings and was hurt by his defense. The left-hander gave up five runs - two earned - four hits, walked three and struck out two. He fell to 3-10 against the Braves since signing a free agent contract with the Mets in 2003.
"It was a matchup as advertised," said Atlanta manager Bobby Cox. "Both threw great. We were lucky to get more than one run off Glavine."
Glavine said he never thought about the matchup with Smoltz during the game.
"When you're out there pitching and trying to win the game, it's difficult to think about that. It's a little more difficult if it's a friend out there. But once the game starts, that's out the window," he said.
"It was vintage Glavine," said Smoltz. "We got a couple of bloop hits and there was a misplay in the outfield. If it weren't for that, we might still be playing."
It was the 194th win for Smoltz, who also has 154 saves. Glavine has 291 career wins.
Both clubs are 4-1. The Mets took the series opener Friday night 11-1.
The Braves batted around and scored three runs - two unearned - in the sixth to take a 5-2 lead.
Andruw Jones led off the inning with a double and went to third on a sharp single to right by Jeff Francoeur. One out later Glavine walked Craig Wilson to load the bases. Matt Diaz hit a sacrifice fly to right that Green dropped.
"I just got turned around," said Green. "I thought the ball was going to break towards the line, got spun around, the wind pushed it the other way and I still thought I had it."
Reliever Pedro Feliciano came on and pinch-hitter Chris Woodward followed with another sacrifice fly. Another run scored when Kelly Johnson drew a walk, loading the bases, and Edgar Renteria beat out an infield single, scoring Wilson, for the 5-2 lead.
New York got back a run in the seventh off reliever Mike Gonzalez on an RBI single by Green, who had three hits.
The Mets tied it at 2 in the fifth on an RBI single by Carlos Beltran, who has hit safely in all five games. His hit scored Jose Reyes, who had walked, stolen second and gone to third on a grounder by Paul Lo Duca. The Mets catcher gave New York a 1-0 lead with a solo homer in the first.
The Braves went ahead 2-1 in the second on a solo homer by Diaz off Glavine. Atlanta scored an unearned run in the first when Johnson reached on an error by first baseman Carlos Delgado. Glavine then walked Renteria and Andruw Jones, loading the bases with one out before Francoeur followed with a run-scoring groundout.
The Mets won their first four games for the first time since 1985, when they opened the season with five straight wins for their best start ever. The Braves opened the season with a three-game sweep of Philadelphia.
Notes: The Mets outscored their opponents 31-3 in the first four games. According to the Elias Sports Bureau, since 1900 only one other major league team began a season with four consecutive victories while outscoring the opposition by at least 28 runs: the 1978 Brewers. The last National League team to do that was the New York Gothams in 1884. (The Gothams became known as the Giants a year later.)