Van Slyke backed starter Dan Haren (6-4), who surrendered two runs on five hits over 5 1/3 innings.
Justin Turner and Tim Federowicz each drove in a run for the Dodgers, who have won three of their last four.
Tony Cingrani (2-7) was roughed up for six runs on seven hits and three walks over 4 2/3 innings in his fifth straight loss.
Ryan Ludwick smacked a solo homer for Cincinnati, which had its two-game winning streak halted.
Van Slyke smoked his first homer of the night to left-center to open the scoring in the second.
Brayan Pena and Zack Cosart singled with two outs in the home half of the second, and both moved up on a wild pitch by Haren. Donald Lutz was then intentionally walked to load the bases for Cingrani, but Haren unleashed another wild pitch before striking out his counterpart as the Reds tied the game.
Turner drove Matt Kemp in with a single in the fourth, and Federowicz added a sacrifice fly to right that plated Van Slyke later in the inning.
Ludwick got one of the runs back, cutting the deficit to 3-2 with his fifth homer of the season to begin the bottom of the fourth.
The Dodgers worked a two-rally in the fifth when Van Slyke hit his second homer of the night and sixth of the season. Yasiel Puig and Kemp walked with two down and Van Slyke followed with a drive to left that increased the LA lead to 6-2.
Billy Hamilton stepped to the plate for Cincinnati with two on and one out in the seventh and grounded into his first double play of the season to end the inning.
The Reds had another chance to chip into the deficit, loading the bases in the eighth with no outs against reliever Brandon League. Ludwick tapped one softly back to League, who threw home to start a 1-2-3 double play. Pena then chopped one to shortstop and the Dodgers escaped the threat unscathed.
Dodgers closer Kenley Jansen, who hadn't pitched in a game since June 2, struck out two in a perfect ninth to secure the win.