Navarro connected for a solo blast in the second inning -- putting the Cubs ahead to stay at 2-1 -- and then added a two-run shot in the fourth and a three-run clout in the seventh.
The Chicago catcher finished 3-for-3 with four runs scored as the Cubs won a second straight over the White Sox in their rain-shortened three-game interleague rivalry series.
Scott Feldman (5-4) handled the White Sox on two runs over six innings, yielding six hits without a walk while striking out seven.
White Sox starter John Danks (0-1) was roughed for four runs (three earned) in his second start since missing more than a year due to shoulder surgery. The left-hander allowed five hits and one walk over four frames.