Lowry, who caused the shock of the first round when he knocked out world number one Rory McIlroy, had no answer for McDowell as he fell to a 3&2 loss on Saturday.
The Portrush man made four birdies to reach the turn four up but saw no further gains on the back nine, with a bogey on the 15th closing the gap by one.
However it was all over on the next hole as both men hit pars.
McDowell now faces Australia's Jason Day, who beat Bubba Watson 4&3.
Meanwhile the remaining ties of the round see Steve Stricker face Ian Poulter, Hunter Mahan take on Webb Simpson and Matt Kuchar against Robert Garrigus.