Niese (10-6) didn't allow a runner past second base after the first inning, scattering five hits. The left-hander yielded no walks and struck out seven in the gem, throwing 70 of his 106 pitches for strikes.
Davis supplied all the offense New York would need on a seventh-inning blast with David Wright aboard.
Edwin Jackson (7-8) absorbed the hard-luck loss despite fanning 11. He surrendered a pair of runs on just two hits while walking one for the National League East-leading Nationals.