With new coach and six-time Slam champion Boris Becker watching him during an official match for the first time, Djokovic appeared tentative early against the Slovakian player, who often appeared content to keep the ball in play.
But as the second-seeded Djokovic's patience level began to drop, his skill level stepped up. He stayed on course for a fifth Australian title, hoping to be the first man to achieve that feat since the Open era began in 1968.
Djokovic also had a strong finish to 2013, entering the tournament on a 24-match winning streak, which followed his loss to Rafael Nadal in last year's US Open final. He's now also on a 22-match winning streak at Melbourne Park.
"It is the first competitive match I've had this season, I haven't played for five or six weeks," Djokovic said. "I was a bit rusty on the court the first two sets. Afterwards it was all working well."
Third-ranked David Ferrer opened with a 6-3, 6-4, 6-4 win over Colombia's Alejandro Gonzalez, and No. 7 Tomas Berdych beat Aleksandr Nedovyesov of Ukraine 6-3, 6-4, 6-3. No. 20 Jerzy Janowicz, a semifinalist at Wimbledon last year, rallied to beat 19-year-old Australian wild card Jordan Thompson 1-6, 4-6, 6-4, 6-2, 6-1 in 3 hours, 16 minutes.
Other men advancing included No. 9 Richard Gasquet, No. 14 Mikhail Youzhny, No. 17 Tommy Robredo, No. 19 Kevin Anderson, No. 23 Ernests Gulbis, No. 29 Jeremy Chardy, No. 32 Ivan Dodig and American Sam Querrey, who defeated Santiago Giraldo of Colombia, 6-3, 6-2, 3-6, 7-6 (3).
"To win this match, in a tiebreak in the fourth set, gives me a ton of confidence," said Querrey, who had 47 winners and 24 aces.