Lannan (2-3), who pitched six seasons for Washington before being demoted to the minors and demanding a trade last year, quieted the Nats on four hits and a pair of walks.
The left-hander struck out four in making his first appearance against his ex-club, snapping the Nationals' four-game winning streak in the opener of a four-game series.
Rollins' run-scoring single in the sixth inning gave Philadelphia a 3-0 lead and turned out to be game-winner after closer Jonathan Papelbon surrendered a pair of runs in the ninth but ultimately hung on for his 19th save.
Dan Haren (4-10) absorbed the loss, surrendering two runs on seven hits over five full frames.
Celebrity Families of 2014 [PHOTOS]