Buckley kicked first-half field goals of 18 and 42 yards for Navy (1-1).
Dobbs' score was also in the first half. The touchdown extended his streak of scoring in all 15 games he's started, but the only other big play the senior made was a 44-yard pass on the final drive of the game, which allowed Navy to run out the clock.
Navy's triple option gained just 193 yards, 109 rushing, after totaling 485 yards in a loss to Maryland on Monday.
Dobbs was held to 44 yards on 25 carries by Georgia Southern's defense.
The Midshipmen's rushing total was the lowest since a 35-yard effort in 2002 against Connecticut.
Georgia Southern, coached by former Navy assistant Jeff Monken, finished with just 109 yards offense, 73 rushing and 36 passing, running its version of the triple option.
In the first half, the Eagles (1-1) gained 23 yards on 21 plays and had just two first downs.
The Eagles more than doubled that on their opening drive of the second half as they drove 49 yards and got a 17-yard scoring pass from Jaybo Shaw to J.J. Wilcox, closing to within 13-7.