World No 2 Djokovic needed just 73 minutes to finish off an embarrassingly one-sided 6-1, 6-0, 6-1 mauling of hapless Italian Paolo Lorenzi.
The second-seeded Serb overcame dropping his serve in the opening game to reel off 18 of the next 19 games, firing seven aces as well as 32 winners against 30-year-old Lorenzi, who has never won a Grand Slam match.
Meanwhile, Andy Roddick, America’s last men’s major champion when he captured the 2003 US Open title, eased past compatriot and qualifier Rhyne Williams 6-3, 6-4, 6-4.
Fourth-seeded Spaniard David Ferrer beat South Africa’s Kevin Anderson 6-4, 6-2, 7-6 (7/3) last night. Ferrer will now face Dutch qualifier Igor Sijsling for a place in the last 32.