"That was a big-time shot that big-time players make," Georgia senior Gerald Robinson Jr. said. "I don't care what year you are classification-wise, when you hit shots like that you're a star."
Caldwell-Pope led the Bulldogs with 20 points on 7 of 15 shooting, including 6 of 12 from 3-point range.
Georgia (12-12, 3-7) earned its first Southeastern Conference road win this season and only its second road victory overall. Robinson added 13 points, including eight in overtime. Dustin Ware had 11.
Mississippi State (19-6, 6-4) was led by Dee Bost's 21 points. The senior guard missed a 3-pointer at the buzzer that could have won the game.
Georgia trailed for much of the afternoon, but Robinson hit a driving layup with 27 seconds remaining that sent the game into overtime.
Georgia won at Humphrey Coliseum for the first time since 2002.
Mississippi State coach Rick Stansbury said his team appeared flat from the opening tip.
"When you're not yourself, it's a fine line and unfortunately today we were on the wrong side of that line," Stansbury said. "... Nowhere in that game did I feel that we got that emotion to where it needed to be. When you don't get to that level, that's what can happen."
Jalen Steele scored 15 points and Arnett Moultrie added 12 as Mississippi State lost the final game of its three-game homestand. Steele missed a 3-pointer just before the buzzer in regulation that would have won the game.
The game was back and forth in overtime with Mississippi State taking a 66-65 lead on Steele's 3-pointer with 1:22 remaining. But Caldwell-Pope responded with his own 3-pointer just seconds later, faking fellow freshman Rodney Hood before making the long jumper for a 68-66 lead with 1:02 left.
"He made a couple of errors early in the game and he's normally not a guy to do that," Georgia coach Mark Fox said. "I had to chew him out a little bit and I think he felt a little guilty after that. He came through for us in a big way."
Robinson missed a free throw with 8 seconds remaining overtime, which gave Mississippi State a chance to tie or win. Bost got a decent look from about just beyond the 3-point line but missed everything and Georgia celebrated the win.
Bost said he was expecting Stansbury to call a timeout in the final seconds, but didn't want to make excuses.
"We didn't bring it, so that's what we get," Bost said.
Georgia was coming off arguably its most impressive game of the season, an 81-59 home victory over Arkansas. And the Bulldogs played well again against Mississippi State, slowing the pace of the game by packing in the defense against MSU's talented frontcourt.
Caldwell-Pope scored 14 points in the first half, helping Georgia shake off a slow start. Mississippi State led 34-31 at halftime.
Caldwell-Pope was quiet for much of the rest of the game, until the big 3-pointer in overtime. He is the team's leading scorer with 14.2 points per game.
Moultrie's been one of the SEC's most consistent players, averaging 17 points and a league-leading 11 rebounds per game. But he didn't find a lot of room to work in the paint against Georgia and had a team-high three turnovers.
"We didn't do anything really different, we just played with heart," Robinson said. "We knew we'd be a little undersized, but it's about playing with pride and putting a body on someone."
Sidney helped offset Moultrie's subpar performance with one of his better outings. The inconsistent 6-10 sophomore contributed 10 points and 12 rebounds for his first double-double of the season.