With Hurricane Irene looming, The Barclays was shortened to 54 holes.
Johnson ended at 19-under-par 194, two shots better than defending champ Kuchar.
The 27-year-old now has won the last two PGA events that have been shortened to 54 holes by weather -- he also won the 2009 Pebble Beach Pro-am.
With his victory in the first event in the FedExCup chase, Johnson jumped into first place, followed by Kuchar. The top 100 on the points list advance to next week's Deutsche Bank Championship.
Brandt Snedeker (10-under 61) and Vijay Singh (68) tied for third place at minus-16, while Jonathan Byrd (67) grabbed sole possession of fifth one shot further back.