Thole drove in a second-inning run on a groundout while Davis and Bay combined for five hits and four runs scored as New York won its fifth straight game.
Ryota Igarashi (1-0) was credited with the win for coming in and striking out Jayson Werth after the Nats had put runners at second and third with two outs in the fifth inning.
Francisco Rodriguez picked up his fifth save with a scoreless ninth.
Zimmermann yielded five runs on nine hits over a 5 1/3-inning start for Washington.
The Nationals lost despite a big night from catcher Wilson Ramos, who homered twice while going 3-for-4 with three RBI.