Patrick Kivlehan's two-run home run to left field highlighted a three-run first inning for Jackson, which dealt Chattanooga its first loss of the series with a 4-2 win Sunday.
The Lookouts dropped to 30-31 in the Southern League's second half but remained a game behind first-place Tennessee, which has lost four straight.
Chattanooga pulled within 3-1 in the second inning on Darnell Sweeney's single to center that scored Alex Liddi and made it 3-2 in the seventh on a homer to right by Bobby Coyle Jr.
Game four of a five-game series in Jackson is tonight at 8:05 EDT.
Steve Smith (2-1, 3.34) is scheduled to start for the Lookouts, with Stephen Landazuri (6-5, 4.13) scheduled for the Generals.