Johnson finished at 11-under 135 as play finally got under way with 36 holes at Kapalua, Hawaii, following three straight days of cancellations due to unrelenting high winds.
He now has a chance to take his seventh career PGA Tour title when play wraps up with 18 holes Tuesday.
Defending Hyundai champion Steve Stricker carded rounds of 2-under 71 and 6-under 67 to claim sole possession of second place at 8-under 138.
One stroke further back at minus-7 was Bubba Watson (70-69).
Sharing fourth at 6-under 140 were Keegan Bradley (71-69) and Brandt Snedeker (70-70).