Toole, who walked four, was pulled after four innings, and reliever Brian Irving kept the no-hitter going until Savannah's Dock Doyle reached on an infield single with one out in the seventh.
The high-chopping grounder was one of only two hits Savannah managed, as GreenJackets reliever Chris Gloor closed out the game with two shutout innings.
Combined with Sunday's 1-0 win in 18 innings, Augusta pitchers have thrown 27 consecutive shutout innings against the South Atlantic League's top team.
"We're throwing the ball good right now," GreenJackets manager Dave Machemer said. "You're always going to expect the best, and right now that's what they're going out and doing."
Dominguez, who beat out a grounder to third baseman Jefry Marte for a single in the first inning, advanced to third on a single from Luke Anders. With runners at the corners, Savannah starter Mark Cohoon tried to pick off Anders at first. Dominguez immediately broke from third and beat the throw home for the first score of the game.
"He threw over to first before that, and I saw it was a slow move," Dominguez said. "So I'm thinking, 'If he does that again, I think I'm going to go.' "
Anders added an RBI sacrifice fly in the fifth inning to drive in Nick Liles, and Evan Crawford scored from third base on a wild pitch in the sixth inning.
GreenJackets second baseman Ryan Cavan went 2 for 3 with a pair of doubles. He also helped turn two double plays to add to the GreenJackets' league-leading total of 47 in 38 games.
Irving (2-0) got the win in relief with just one hit and one walk in three scoreless innings, while Gloor picked up his second save of the season.
Cohoon, who entered the game as one of the top starters in the league with a 4-0 record and 1.76 ERA, got his first loss of the year after giving up two earned runs and seven hits over five innings pitched.
The shutout was the sixth of the season for the GreenJackets pitching staff, and four have come against Savannah.
Augusta (23-15) pulled to within one game of Savannah (24-14) in the South Atlantic League's Southern Division.