Jasmine James added 11 points for the Lady Bulldogs (26-6), who will face No. 5 seed Iowa State in their next game on Monday night.
Georgia led 38-36 with 15 minutes remaining before going on a 21-6 run to grab control and earn a bit of redemption after being upset by Marist in the first round a year ago.
Torry Hill led 13th-seeded Montana (24-8) with 11 points. But on a night the Lady Griz needed to hit all their open looks, they shot just 29 percent and committed 20 turnovers.
The matchup featured two of the most successful coaches in women's college basketball. Montana's Robin Selvig and Georgia's Andy Landers had combined for 1,618 wins at their respective schools coming into Saturday's game and Selvig was looking for an upset that would move him within one victory of joining Landers in the 800-win club.
That upset bid was tossed aside by Georgia's impressive second-half charge, mostly thanks to the Lady Bulldogs' defense. Georgia entered the tournament among the best in the country giving up just 53.3 points per game during the regular season.
The stout defense was on display as the Lady Bulldogs took command, holding Montana to just two field goals in a 12-minute span. Montana's drought was finally broken when Hannah Doran hit a 3-pointer with 2:35 left.
Georgia was stunned when it was knocked out of the tournament in the first round a year ago and vowed it wouldn't overlook its opening opponent. Still, it was a struggle to shake the pesky champions of the Big Sky Conference, who were trying for their first NCAA win since 1995.
The Lady Griz even had a chance to take the lead early in the second half.
Alyssa Smith hit a 3 to open the second half as Montana closed to 32-28, the closest it had been since it was 8-4. After Hassell split a pair of free throws, Baker hit a 17-footer and the Lady Griz were within three. Baker then split a pair of free throws and Georgia's lead was just 33-31.
Griffin answered with a corner 3-pointer and Shacobia Barbee scored on a drive to push the lead back to seven, but Baker scored and Jordan Sullivan hit a 3. Montana committed a turnover with a chance to pull even or take the lead.
That proved to be as close as the Lady Griz would get. Following a timeout, Georgia ran off 13 of the next 17 points to take a 51-40 lead with 9:10 remaining. Anne Marie Armstrong hit a corner 3-pointer, Erika Ford scored off a steal and Tamika Willis scored in the lane to extend the lead to eight. James then hit a pair of short jumpers and Willis scored underneath to run the advantage to double digits.