With the game tied 4-4, Paul led off the ninth by smacking a pitch from Shawn Camp (3-6) into the right field corner, easily cruising into third base.
Then with the Cubs outfielders drawn in, Hannigan followed by lofting a fly ball that fell into left field for the game-winning hit, enabling the National League Central-leading Reds to take three victories in a four-game set with Chicago.
Hannigan finished with two RBI while Jay Bruce went 2-for-4 with a run-scoring single for Cincinnati, which won for the eighth time in nine contests overall.
Aroldis Chapman (5-4) tossed a scoreless ninth to get the victory in relief of starter Mat Latos, who allowed four runs (two earned) on six hits over eight frames.
The Cubs' Alfonso Soriano collected a pair of RBI, including a run-producing groundout in the eighth that forged a 4-4 tie.