He started with a single in the third and then sandwiched a walk in between a double and an eight-inning triple.
The triple was punched the other way and right fielder Bryce Harper seemed to have a hard time battling the sun as the ball bounced passed him.
"My last one, hitting the ball to right field like that, that's where I need to be," Bryant said. "That's when I know I'm going good, when I'm driving the ball to right field. I put a really good swing on that, so I was pleased with that."
Bryant scored twice on the day, including what ended up being the winning run on a two-run single by Chris Coghlan in the fifth inning. In the sixth, Starlin Castro singled in Bryant for the Cubs' final run.
"Well, the big thing is pitch selection, controlling the strike zone," manager Joe Maddon said. "He's done a really great job with that. There will be moments where he may chase for an at-bat or two, but he's able to bring it back in order. And you're seeing the year he's having based on the fact that he's really increasing his plate discipline."
Bryant's average jumped to .282 with the three-hit performance. He remains at seven home runs but added his second triple and eighth double.