Ludwick's two-run shot in the second inning erased an early 1-0 deficit, putting Cincinnati ahead for good, and Frazier's two-run single in the sixth gave the Reds an 8-3 advantage.
The pair combined to go 6-for-9 with five runs scored and six RBI as National League Central-leading Cincinnati evened its four-game series at one win apiece.
Homer Bailey (10-7) allowed four runs on nine hits over 5 2/3 innings and contributed a run-scoring single en route to the victory.
Aroldis Chapman was called on to record the final four outs for his 26th save after the Cubs scored four times off Cincinnati's bullpen.
Chicago starter Justin Germano (1-2) was rocked for six runs (four earned) on seven hits in a 5 2/3-inning effort.