Djere recorded 18 aces and benefited from four double faults by Ruud to win the match in 2 hours, 7 minutes.
Also on Wednesday, second-seeded Cameron Norrie of Great Britain survived a scare before seizing a 6-4, 6-7 (4), 6-3 win over Czech qualifier Jiri Lehecka.
Argentine Diego Schwartzman wasn't as fortunate, as he dropped a 6-1 decision in the first set to Jenson Brooksby before retiring in the match due to a thigh injury.
Adelaide International 2
Australian Thanasi Kokkinakis fired 17 aces to seize a 6-4, 3-6, 6-3 win over top-seeded Andrey Rublev of Russia in a second-round match in Australia.
Lucky loser Soonwoo Kwon of South Korea overcame a first-set misstep to upend second-seeded Pablo Carreno Busta, 3-6, 6-4, 6-4.
Fourth-seeded Roberto Bautista Agut of Spain and sixth-seeded Miomir Kecmanovic of Serbia needed three sets to win their respective second-round matches, while seventh-seeded Alejandro Davidovich Fokina breezed to a 6-3, 6-3 victory over Australian John Millman.
Unseeded Brit Jack Draper notched a 6-4, 6-4 win over eighth-seeded Tommy Paul.