Kimbrel gave up a leadoff single to Roger Bernadina and walked Zack Cozart to open the ninth. Kimbrel struck out Brayan Pena and Chris Heisey before earning his seventh save on Joey Votto's groundout.
Freeman made a long stretch at first base for Chris Johnson's throw from third base on Heisey's groundball. Reds manager Bryan Price challenged first base umpire Vic Carapazza's ruling that Freeman's foot remained on the bag. The call was confirmed, ending the game.
''Freddie did a terrific job staying on the bag,'' said Braves manager Fredi Gonzalez. He acknowledged he was nervous about the challenge before seeing the replay on the video board ''and I felt kind of relaxed.''
Price said that when looking across the field he thought he saw ''a huge gap'' between Freeman's foot and the bag. He said he agreed with the confirmed out call after seeing the replay.
''I had a chance to come up here and look at our own video, which is what they're getting in New York, and it was a confirmed out call,'' Price said. ''They got the call right in the end, which is what we're looking for.''
Two Cincinnati players left the game with injuries. Third baseman Todd Frazier was pulled in the fifth with tightness in his left leg. Catcher Devin Mesoraco strained his left hamstring and stumbled after rounding third base in the seventh, before limping across home plate.
Price said he was protecting Frazier, who had previous tightness in his groin.
Santana (3-0) gave up four runs on nine hits in 6 2-3 innings.
Following singles by B.J. Upton and Freddie Freeman off Homer Bailey (1-2) in the first inning, Justin Upton hit his team-leading sixth homer. He leads the team with 15 RBIs.
''We've seen him do this before and carry us for a while,'' Gonzalez said.
In 2013, Justin Upton led the majors with 12 homers in April, becoming the fastest player in Braves franchise history to reach the mark. He has hit 35 homers in April for his career, his highest total for any month.
''I'm just getting it going,'' said Upton, who is hitting .296 and leads the team with 15 RBIs.
Freeman had three hits for Atlanta to shake a mini-slump.
B.J. Upton, who was hitting .205, had one hit in his first game wearing prescription glasses.
''We'll see how the glasses work and if I'll keep them,'' he said. ''I could see the ball better on both sides of the plate. It was good tonight.''
Bailey allowed five runs on nine hits in six innings. He allowed at least four earned runs for the fourth time in five starts this season and has a 6.15 ERA.
The Braves increased their lead to 4-0 in the second on Jason Heyward's RBI single. Evan Gattis drove in a run in the third for a 5-0 lead.
Jay Bruce had a run-scoring single in the Reds' two-run sixth. Cincinnati added two more in the seventh, knocking Santana out of the game. Mesoraco scored on Billy Hamilton's double. Votto had a run-scoring single off Luis Avilan.
A strong defensive play by right fielder Jason Heyward helped Santana in the first inning.
Votto doubled with one out in the first and moved to third on Phillips' bloop single. Votto was thrown out at the plate on a strong throw by Heyward on Jay Bruce's fly ball. Votto, sliding head-first, was tagged out in the batter's box and never reached the plate.
NOTES: Price said closer Aroldis Chapman, recovering from facial fractures and a mild concussion when hit by a line drive on March 19, will throw 35 to 40 pitches in batting practice on Saturday. If it goes well, it should be Chapman's final test before he is cleared for a minor league rehab assignment. ... Braves RHP David Hale will look for his first win of the season when he faces Reds RHP Mike Leake on Saturday.