The Swiss top seed, who had a bye in the first round, took last year???s trophy before claiming his maiden Grand Slam title at the Australian Open.
He continued to warm-up for the upcoming tournament in Melbourne by producing a ruthless display against the Croatian teenager, who soon trailed 5-0 in the opener.
Coric held serve in the sixth game, but Wawrinka quickly regained control to secure the set.
The second went on serve until the world No 4 seized a break in the seventh game and soon booked his place in the next stage.
During a dominant display, he won 24 out of 26 points on his first serve, and prevented Coric from claiming a single break point.
He will next play eighth-seed Gilles Mueller, who completed a routine 6-4 6-3 win over Elias Ymer.
Fourth-seed David Goffin was made to work much harder for a 6-0 4-6 7-6 victory against Ricardas Berankis as he also advanced to the last eight.??