Johnson raced into a two-up lead after two holes, courtesy of some fine approach play. He nearly holed an iron into the second green, leaving himself with just inches for his birdie.
The American was three up by the time the players reached the fifth hole, but the Northern Irishman was able to claw a hole back to cut his deficit to two.
A par was good enough to see Johnson restore his three-up advantage at the seventh.
McDowell has not been able to settle into the match, but nailed his approach to the ninth to help him card a birdie.
That means that Johnson leads by two as they tee up on the 10th.