Freeman followed an RBI double in the first inning with three straight singles as he raised his average for the spring to .356.
Freeman hit .319 with 109 RBIs last season and recently signed an eight-year $135 million contract.
''I don't know if I can ask him for more,'' manager Fredi Gonzalez said. ''That was a pretty darn good season he had last year. . If he can keep duplicating it year after year, that contract is going to be cheap.''
Alex Wood allowed one run and six hits over six innings while striking out four. It was the first earned run the left-hander has allowed in 20 innings this spring.
Uggla's homer was a two-run drive in the fifth inning and Red Sox starter John Lackey was relieved one batter later after allowing five runs and 10 hits. Lackey struck out six.
Uggla, who slumped to .179 last season, leads the Braves this spring with four homers and 12 RBIs. He is batting .262.
Minor leaguer Derrick Mitchell added a sacrifice fly for Atlanta.
Braves: Wood, who is now entrenched in the rotation after also pitching out of the bullpen as a rookie, threw 95 pitches on a warm day in his second game against the Red Sox this spring.
''I was battling there a couple of innings, but I felt good,'' the second-round draft choice in 2012 said.
''Woody was outstanding,'' Gonzalez said. ''It was a good test for him.''
Red Sox: Lackey has a 9.49 ERA for three spring starts, but feels that he is on track.
''It's spring training. I'm not really concerned about a lot right now,'' he said. I'm just building up arm strength. I feel fine.''
Lackey has one more spring start and would like to build to 90 pitches. The veteran right-hander threw 83 against the Braves.
''I'd like to go into the season not on a pitch count,'' he said.
Simmons' homer came in the fourth inning right after Lackey made a dive and flipped to first to get Jordan Schafer on a bunt, and just before Freeman drilled him on the backside with a liner.
''It got me on the thigh,'' he said. ''I was fine.''
Red Sox: Left-handed reliever Craig Breslow is slated to make his spring debut Monday after throwing 20 pitches of batting practice on Friday.
''By all accounts, it was a good day for him,'' manager John Farrell said.
Breslow started last season on the disabled list, but was still 5-2 with a 1.81 ERA in 61 games.
''It takes him longer than most pitchers to get ready,'' Farrell said.
Braves: Catcher Evan Gattis' sore right quadriceps is better, and he expects to play by Monday.
''Just taking it slow to be safe,'' he said. Gattis, who was hurt circling the bases, caught a bullpen session Saturday and did running trials.
Julio Teheran, who was 14-8 with a 3.20 ERA last year as a rookie, will get the opening-day start for the Braves.
Gonzalez told Teheran on Saturday he'll start on March 31 in Milwaukee. The Braves didn't have much choice after a string of injuries this spring.
Kris Medlen and Brandon Beachy are sidelined because of elbow-ligament transplant surgery. Ervin Santana, who signed late as a free agent, and Mike Minor (shoulder) won't be ready to join the rotation until mid-April.
''I was waiting until they told me,'' Teheran said. ''I'm very happy. It's a great honor to pitch on opening day. Hopefully next year and in a couple of years I'll still be the opening day starter.''