Kendrick (11-12) stifled Washington on four hits, walking one and striking out four while tossing 64 of his 100 pitches for strikes.
Phillippe Aumont earned his second save and Darin Ruf delivered a two-run triple for the Phils, who claimed the opener of a season-ending three-game series.
John Lannan (4-1) absorbed the hard-luck for the Nationals, who nevertheless won their first NL East division championship when the Atlanta Braves fell to Pittsburgh earlier in the evening.
The title was the first for a Washington-based baseball team since the Washington Senators won the 1933 American League championship.
Celebrity Families of 2014 [PHOTOS]