Maten had a career-high 25 points while Mann chipped in with a season-high 21 points with both totaling seven rebounds each. Georgia (14-9, 7-5 SEC) led from start to finish.
Mississippi State (10-14, 3-9) had its lowest scoring output of the season.
Quinndary Weatherspoon had 17 points to lead Mississippi State and Craig Sword had 13 points. Mississippi State shot just 30.9 percent while Georgia made 46.3 for the game and 54 percent in the second half.
"We expected a hard-fought game so our guys were ready to play coming off the (Kentucky) loss," said Georgia head coach Mark Fox. "(Our zone defense) was effective at times and we stayed with that a little longer than previous games. We felt like our team was exhausted at shoot-around today so we decided to play a little more zone."
Maten scored six straight points to open the second half as Georgia stretched its lead to 38-21. Georgia led by as many as 22 points mid-way through the second half before Mississippi State reeled off a 10-0 run to cut the lead down to 51-41.
Mississippi State would not get any closer until scoring with seven seconds left to provide the final margin.
Maten was 10 of 16 from the field and 5 of 7 at the free-throw line en route to his career night.
"We did a good job on defense tonight," said Maten. "We limited them and we were strong on the glass tonight. Our zone matched up well with their offensive plays really well."
Both teams struggled on offense in the first half but it was Georgia's dominance on the backboards that was the difference. Mississippi State shot just 25.9 percent in the opening half while the visiting Bulldogs were only at 40.6 percent.
However, Georgia held a 27-14 advantage in rebounding and nine offensive rebounds led to 10 second-chance points for Georgia in the first half. Maten had five straight points to give Georgia its biggest lead at 30-17 late in the first half.
Georgia led 32-21 at the break and Maten had 15 points in the first half.
"I thought Georgia really took it to us on both ends of the floor," said Mississippi State head coach Ben Howland. "We struggled to score and took too many 3s (8 of 28). When you look at our inside presence, we had two free throws attempted total from our four inside guys.
"I thought the physicality Georgia brought tonight and the way they sealed us up inside were real problems for us."
Georgia held a decisive 45-35 advantage on the backboards and Derek Ogbeide led Georgia with 13 rebounds. Led by Maten and Mann, Georgia outscored Mississippi State 34-14 in the paint.
Mississippi State: Mississippi State's 21 points in the first half was the lowest total of the season for the Bulldogs. Mississippi State has now dropped four straight home games to Georgia dating back to 2010. Gavin Ware now has 820 career rebounds, good for fourth-most in school history.
Georgia: The SEC's top four active scorers were on the floor together Saturday night. Mississippi State senior Craig Sword and Gavin Ware rank first and third, respectively, as the SEC's top active scorers along with Georgia's Charles Mann and Kenny Gainers at No. 2 and No. 4, respectively.
Mississippi State hosts Vanderbilt on Tuesday.
Georgia hosts Florida on Tuesday.