The top-seeded Djokovic needed just 84 minutes to dispose of Andrey Kuznetsov, 6-0, 6-1, 6-4, at Rod Laver Arena.
Djokovic's next step toward becoming the second man to win five Aussie Open titles comes Saturday against the winner of the match between No. 31 Fernando Verdasco and Go Soeda.
The fourth-seeded Wawrinka extended his winning streak at this major to nine with a 7-6 (7-4), 7-6 (7-4), 6-3 win over qualifier Marius Copil.
Fifth-seeded Kei Nishikori went down early against Ivan Dodig but wound up pulling out a 4-6, 7-5, 6-2, 7-6 (7-0) victory.
Feliciano Lopez, seeded 12th, trailed by two sets to Adrian Mannarino, staved off a match point in the third and advanced when Mannarino retired due to heat exhaustion in the fourth. Lopez was leading 4-0 in the fourth prior to Mannarino calling it quits.
American John Isner advanced to the third round with a 6-4, 7-6 (7-4), 4-6, 6-4 decision over Andreas Haider-Maurer. The 19th-seeded Isner plays the winner of the match between No. 13 Roberto Bautista Agut and Gilles Muller.
Another American also moved on, as Steve Johnson pulled off a mild upset with a 6-3, 6-4, 6-2 pasting of 30th-seeded Santiago Giraldo. Johnson next squares off against Nishikori, who was last year's U.S. Open runner-up.