Last season, Wickman gave up a game-ending grand slam to Dunn that gave the Reds a 9-8 win over Cleveland.
"We have to forget what happened here, go to St. Louis and try to get started on a good note," Wickman said.
Mark Teixeira homered and Chipper Jones matched a career high with five RBI, but that wasn't enough to keep the Braves from their second three-game losing streak in eight days. Atlanta fell three games behind San Diego, the NL wild card leader.
With one out in the 12th, Brandon Phillips reached on an error by Wickman (3-3), who couldn't handle a flip to first from Teixeira. Dunn followed with a 417-foot drive halfway up the seats in right-center for his 35th homer of the season, giving the Reds their fourth win in five games.
"I tried to run one in on him, figuring he might be looking away," Wickman said about his 2-1 fastball. "I tried to sneak one by him."
Dunn left the clubhouse before reporters entered. Reds manager Pete Mackanin said his first concern when he saw Dunn start to swing was that he might spoil a potential stolen base by Phillips.
"Phillips had such a good jump that I said, 'Please don't foul this off,"' Mackanin said. "As soon as I saw the ball in the air, at that point, I didn't care any more."
Mike Gosling (2-0) had a strikeout in a perfect 12th for the win.
"Their bullpen pitched great the whole series," said Atlanta manager Bobby Cox, who was ejected after the second inning for arguing - extending his major league record.
Gosling kept the Reds in the game after they failed to score with runners on second and third with nobody out in the 11th.
"While I was warming up, I kept reminding myself about what I had to do," he said. "I wanted to stay ready and not relax, thinking we were going to score."
Hamilton's three-run shot, his 17th homer this season and second in two games, capped Cincinnati's five-run second that started with Phillips' leadoff single and Scott Hatteberg's one-out double. After Javier Valentin walked, Encarnacion drove in Hatteberg with a ground-rule double.
Teixeira cut Cincinnati's lead to 5-2 with a homer leading off the fourth, his third of the four-game series and 10th since joining Atlanta on July 31.
Jones tied the score in the fifth with a three-run shot following consecutive walks to Willie Harris and Kelly Johnson. Jones' 21st homer of the season chased Cincinnati starter Elizardo Ramirez, who gave up five hits and five runs with four walks in 4 1/3 innings.
Jeff Keppinger and Ken Griffey Jr. hit consecutive two-out doubles in the fifth to give the Reds a 6-5 lead, but Johnson and Jones hit back-to-back doubles to tie it in the seventh. Teixeira followed with a single to give Atlanta a 7-6 lead, but Encarnacion tied it in the bottom half with a leadoff homer, his ninth of the season and first in 56 at-bats since Aug. 4.
Griffey's extra-base hit was his 1,094th, breaking a tie with Hall of Famer Dave Winfield for 16th place on the career list.
The Braves took a 1-0 lead in the first on Harris' leadoff walk, Johnson's sacrifice and Jones' double.
Jones had five RBI for the 14th time in his career. His homer got Atlanta starter and former Reds minor leaguer Buddy Carlyle off the hook after Carlyle allowed six runs and six hits in five innings.
- Atlanta shortstop Edgar Renteria was placed on the 15-day disabled list after aggravating his sprained right ankle. He was activated on Wednesday. INF Martin Prado was recalled from Triple-A Richmond.
- Plate umpire Jerry Lane ejected Cox after the second inning and hitting coach Terry Pendleton in the sixth.
- The Reds honored former catcher Johnny Bench, second baseman Joe Morgan and Griffey in pregame ceremonies for being voted by fans to the all-time Rawlings Gold Glove team.