Kendrick (7-9), one of seven pitchers used by Philadelphia, allowed four hits and struck out three to help the Phillies win for the fifth time in the last seven games.
Tyler Moore homered for Washington, which lost its second straight.
Moore snapped Kendrick's 21 2/3 innings scoreless streak with a two-out, two-run homer in the seventh. Kendrick retired the first two batters in the frame before walking Kurt Suzuki. Moore, pinch-hitting for Edwin Jackson, launched an 0-1 sinker into the seats in left to pull Washington within 3-2.
Jackson (11-8) gave up three runs on seven hits with eight strikeouts and two walks in six innings to fall to 0-4 with a 5.32 ERA in four career starts against Philadelphia.
Jonathan Papelbon earned his 28th save in 31 chances with a scoreless ninth.
Rollins gave the Phillies a 3-0 lead in the fourth when he lined an opposite-field, two-out single to left off Jackson to score John Mayberry Jr. and Laynce Nix, who barely beat the tag of Suzuki with an elusive head-first slide at the
Chase Utley's RBI single in the first had given Philadelphia a 1-0 lead. The Phillies were positioned to add on to the lead, with runners on first and third and no outs, but Ryan Howard struck out and Domonic Brown grounded into an inning-ending double play.
The Phillies used four pitchers in a scoreless eighth inning. Antonio Bastardo started the frame with a strikeout of Bryce Harper and was followed by Josh Lindblom, who walked Ryan Zimmerman. Raul Valdes then relieved Lindblom and surrendered a single to Roger Bernadina before striking out Adam LaRoche. With two outs and runners on first and second, B.J. Rosenberg followed Valdes and struck out Jayson Werth to end the frame.
The Phillies padded their lead in the bottom of the inning. Utley walked, stole second and scored on Howard's single to right that put Philadelphia up 4-2.
Michael Morse left the game in the first inning with a contusion on his right hand after being hit by a Kendrick pitch.
Ian Desmond was a late scratch due to a right knee injury suffered in Wednesday's game against Atlanta. Desmond, who was replaced at shortstop by Danny Espinosa, was available to pinch-hit.