There were also wins on day one for seeds Tomas Berdych, Nicolas Almagro, Stanislas Warwinka and Kei Nishikori.
Mathieu, a former top-12 player, held his own for much of the second and third sets but Djokovic always appeared in control on his first competitive appearance on Rod Laver Arena since his thrilling near six-hour final win over Rafael Nadal last year.
The Serbian set the tone in the opening game by breaking and claimed the Mathieu serve once again courtesy of a stunning backhand pass to establish a 4-1 first-set advantage. He duly saw out the set and then broke again to open the second.
Mathieu threatened an immediate response but some booming serves from Djokovic enabled him to escape from 0-40. Serve held sway for the rest of the set as it did in the third until Djokovic upped his level with a series of stunning winners to take a 6-5 lead.
And from there, there was no way back for Mathieu as Djokovic advanced to a meeting with American Ryan Harrison.
Djokovic enjoyed his return to the biggest arena at Melbourne Park.
He said: "It's great to be back in Melbourne, this is by far my most successful court in my grand slam career.
"Twelve months ago I played a six-hour final here so it's amazing to be back."
Czech Berdych, seeded five in Melbourne, enjoyed a routine 6-3 7-5 6-3 win over Michael Russell but Almagro was pushed all the way by American qualifier Steve Johnson.
Johnson matched the 10th-seeded Spaniard for much of their three hour, 10 minute-encounter before Almagro's greater experience proved key in his 7-5 6-7 (4/7) 6-2 6-7 (6/8) 6-2 victory.
Wawrinka beat German Cedrik-Marcel Stebe in straight sets while Nishikori hit back from dropping the opener to see off Victor Hanescu.