Anthony Rizzo had two RBI, and Kris Bryant drove in the go-ahead run with an RBI single to break up Stephen Strasburg's no-hitter as the Cubs seized home field advantage in the series.
Kyle Hendricks pitched seven shutout innings to help the Cubs to their first win of the playoffs.
Stephen Strasburg was in top form through the first five innings of the game, striking out eight batters, but after Javier Baez reached on an error in the sixth inning, Bryant drove in his teammates to give the Cubs a lead they would never relinquish.
The two pitchers cruised through the first five innings, as Strasburg held the Cubs without a hit and Kyle Hendricks pitched out of a couple of jams to keep the Cubs in the game.
That all changed in the sixth inning, as the Cubs finally broke through and took the lead. With Javier Baez on second base, Kris Bryant smacked a single to right field, scoring Baez and giving the Cubs a 1-0 lead.
Anthony Rizzo then smacked a single of his own, scoring Bryant to extend Chicago's lead to 2-0.
That lead stayed intact until the eighth inning, when Rizzo struck again. With Jon Jay on second base, Rizzo sliced an opposite field double into left field, giving the Cubs a three-run lead.
Carl Edwards Jr. and Wade Davis combined to throw two scoreless innings in the eighth and ninth, and the Cubs cruised to a 1-0 series lead.
The Cubs will look to seize full control of the series on Saturday afternoon when they take on the Nationals in Game 2. Jon Lester will pitch for the Cubs, with the game scheduled to start at 4:38 p.m.