Frazier's two-run single capped a three-run fourth inning that put Cincinnati ahead to stay and Joey Votto (3-for-5) smacked a run-scoring double in the seventh for a 5-3 advantage.
Mat Latos (3-0) earned the victory despite going just five innings, allowing three runs on six hits and three walks while striking out six.
Sam LeCure and Sean Marshall combined for three innings of one-run ball out of the bullpen and J.J. Hoover fired a 1-2-3 ninth for his second save to nail down the Reds' three-game sweep at Wrigley Field.
Chicago starter Edwin Jackson (0-5) was touched for four runs on eight hits over five frames.
Alfonso Soriano drove in two runs for the Cubs, who dropped their sixth in eight games overall.