Kendrick (7-9) brought a 15-inning scoreless stretch into the contest and kept it going until Tyler Moore hit a two-run homer in the seventh that cut Washington's deficit to 3-2.
A parade of six Philadelphia relievers then held the Nationals in check over the final 2 1/3 innings, with Jonathan Papelbon working around a leadoff single in the ninth to record his 28th save.
Ryan Howard completed the scoring with an RBI single in the eighth that delivered Utley.
Edwin Jackson (7-9) suffered the loss despite striking out eight over six innings.
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