Glavine (6-0) struck out three and walked one as the Braves won for the 10th time in 13 games.
It was the 11th career shutout for Glavine, who threw only 94 pitches. He lowered his earned-run average to 3.39.
Glavine was perfect for five innings before Wilfredo Cordero opened the sixth with a line drive single to right.
Gant hit his eighth home run of the season in the second inning against Expos starter Jeff Shaw (0-1). Shaw left for a pinch-hitter after five innings.
San Francisco 6, Houston 3--Willie McGee's two-run triple keyed a five-run first inning, and Matt Williams took the league lead with two runs batted in as the Giants completed a sweep of the Astros at San Francisco.
The victory gave San Francisco a 3 1/2-game lead in the West over Atlanta.
Jeff Brantley (3-3) gave up seven hits and walked one in six-plus innings.
The Giants sent eight to the plate in the first against Pete Harnisch (4-2).
After that, Harnisch settled down and didn't give up a hit over the next five innings. In six innings, he gave up four hits and three earned runs, struck out four and walked one.
Houston made it 5-1 when Jeff Bagwell led off the fourth with a single and scored on Luis Gonzalez's sacrifice fly.
In the fifth, Brantley hit Craig Biggio with a pitch. Then Steve Finley and Bagwell had consecutive singles, the latter scoring Biggio.
Cedeno hit his first homer, against Rob Beck in the ninth, to make it 6-3.
San Diego 7, Colorado 3--Greg Harris won his third consecutive start despite giving up three home runs at San Diego as the Padres pounded former Padre minor leaguer Lance Painter in his major league debut.
Harris (4-5) finished with a six-hitter. He struck out five and walked two.
Painter, brought up Monday from triple-A Colorado Springs, gave up six runs and 12 hits in 4 1/3 innings. Fred McGriff drove in three runs and Derek Bell had three hits and two RBIs, including his sixth home run.
Daryl Boston had Colorado's first two-homer game with leadoff drives in the fourth and sixth innings, his first two home runs this year. Former Padre Jerald Clark hit a leadoff homer in the fifth.
Still, that wasn't enough to keep the Rockies from losing for the 13th time in 15 games. Painter fell behind 3-0 when seven of the first 12 batters reached base.
Florida 5, Philadelphia 3--Second baseman Mickey Morandini's two-out error led to three unearned runs in the seventh inning at Miami.
The Marlins, who had been 0-16 when trailing after six innings, avoided their first series sweep.
Morandini bobbled Junior Felix's easy grounder with runners at first and second. Chuck Carr walked on a 3-2 pitch from Mark Davis (1-2), forcing in a run and tying the game, 3-3. Rich Renteria put Florida ahead with a two-run single to shallow center.
Richie Lewis (2-0) pitched two scoreless innings for the victory. Bryan Harvey pitched 1 1/3 perfect innings for his 12th save in 13 chances.
Wes Chamberlain and Pete Incaviglia gave Philadelphia a 3-1 lead with home runs against Chris Hammond.
The homers were the only hits given up by Hammond, who left after five innings with upper-back spasms. He is not expected to miss a start.
Chicago 5, St. Louis 3--Mark Grace drove in two runs and broke an eighth-inning tie with a run-scoring single to lead at St. Louis.
Relief pitcher Rob Murphy (1-4) helped the Cubs get started, covering the bag late on pinch-hitter Willie Wilson's leadoff infield grounder, then throwing late to second on Jose Vizcaino's sacrifice bunt.
The runners were on the move when Grace singled to right for his 20th RBI in 17 games. Grace is 25 for 64 (.391) during that span.
Mike Morgan (3-6) worked seven innings and gave up three runs on eight hits and avoided becoming the major leagues' first seven-game loser.