The Phillies, winners of two straight and six of eight, got a solid start from Kendrick (3-6), who had gone 2-11 in his previous 20 starts since last Aug. 11.
Kendrick allowed six hits and two runs with one walk and six strikeouts in seven innings.
Not since last July had Kendrick won two straight starts. The right-hander was coming off a 7-3 victory last week against San Diego.
Atlanta has lost seven of 11 and 13 of 21.
Ervin Santana (5-4) continued to struggle, giving up eight hits and four runs — three earned — with three walks in six innings. Santana, who struck out five, is 1-4 with a 6.17 ERA in his last seven starts.
The Phillies took a 2-0 lead in the first when Rollins led off with a double and Howard hit his 13th homer. In 71 career games at Turner Field, Howard is hitting .277 with 20 homers and 69 RBIs.
Philadelphia, which had its leadoff hitter reach safely in eight innings, went up 4-0 in the fourth. Dominic Brown led off with a walk, advanced to third on Reid Brignac’s double and scored on a passed ball by Gerald Laird. Brignac, who moved to third on the passed ball, scored on Cesar Hernandez’s RBI single.
Atlanta made it 4-1 in the fourth on Jason Heyward’s RBI single.
The Braves cut the lead to 4-2 in the seventh when Chris Johnson led off with a double, moved to third Andrelton Simmons’ single and scored on Laird’s double-play groundout.
Simmons, named last year’s top defender in the NL, had a rare two-error inning in the ninth that helped former Sprayberry High School star Marlon Byrd reach second on an infield single and score from third on Brown’s fielder’s choice grounder for a 5-2 lead.
Closer Jonathan Papelbon recovered from a blown save Monday to record his 16th save in 18 chances. Papelbon retired pinch-hitter Ryan Doumit on a lineout, Tommy La Stella on a groundout and Johnson on a lineout.
NOTES: The Braves announced that LF Justin Upton left the game after six innings because of dizziness. ... Philadelphia CF Ben Revere missed the game with a sore knee after hitting the wall in Monday’s 6-1, 11-inning victory. Manager Ryne Sandberg said Revere is day-to-day. John Mayberry Jr. started in Revere’s place. ... Phillies LHP Cliff Lee, on the DL since May 20 with a strained elbow, threw off a mound before the game. ... Phillies 2B Chase Utley walked as a pinch-hitter in the eighth. ... Braves RHP David Carpenter was placed on the 15-day DL with a strained right biceps. RHP Pedro Beato, recalled from Triple-A Gwinnett, pitched a scoreless seventh, but walked the bases loaded in the eighth. ... Braves C Evan Gattis, who got the night off, has a franchise-long 16-game hitting streak for a catcher. Del Crandall, in 1958, and Joe Torre, in 1967, had 15-game streaks.