Samardzija (7-11) hurled his second complete game of the season and third of his career, yielding one run. The right-hander didn't issue a walk and struck out five in the 105-pitch gem.
Schierholtz belted a three-run homer in the first, added an RBI double in the third and capped his big night with a two-run shot in the seventh as the Cubs rolled to a win the first of a four-game series.
Murphy, meanwhile, socked a solo homer in the fourth and a two-run clout in the eighth.
Dioner Navarro contributed a three-run blast for the Cubs.
Nats starter Jordan Zimmermann (14-7) was lit up for eight runs on seven hits in a five-inning effort.
Wilson Ramos went deep for Washington's only run.