After downing Colombian Alejandro Falla in round two, Wawrinka was given a free ride through the third round when scheduled opponent Vasek Pospisil pulled out with a back injury.
But he quickly erased any concern that the scarcity of recent court time had taken the edge off his game.
Wawrinka controlled the first set against Robredo and was similarly dominant in the second, except when a touch of tension crept in as he tried unsuccessfully to serve it out at 5-4.
But the Swiss regained top touch in the tiebreak, repeatedly roaring with satisfaction as he reeled off seven of the last eight points, wrapping it up with scorching forehands on the final two of those.
In the third set, Wawrinka saved two break points at 4-4, then came from 4-2 down in the tiebreak.
World No.8 Wawrinka's win means he could overtake No.6 Roger Federer to become the top-ranked Swiss player for the first time in his career, if Federer falls short of the semi-finals.
It also earns Wawrinka a meeting with Djokovic, who is on a 25-match winning streak at Melbourne Park and has won their past 14 encounters.
That bare statistic hides the extent to which the Swiss pushed the Serb in their two meetings that mattered most last year.
In the Australian Open fourth round, Wawrinka played brilliant tennis in a memorable five-hour five-setter against Djokovic, which the Serb won 12-10 in the fifth set.
Djokovic also had to come from two sets to one down to overcome the Swiss in the US Open semi-finals, Wawrinka's sole appearance in the last four of a major so far.
Today's schedule
Rod Laver Arena
Dominika Cibulkova (20), Slovakia, vs. Maria Sharapova (3), Russia
Sloane Stephens (13), United States, vs. Victoria Azarenka (2), Belarus
Rafael Nadal (1), Spain, vs. Kei Nishikori (16), Japan
Night Session
Jo-Wilfried Tsonga (10), France, vs. Roger Federer (6), Switzerland
Agnieszka Radwanska (5), Poland, vs. Garbine Muguruza, Spain
Hisense Arena
Bob and Mike Bryan (1), United States, vs. Eric Butorac, United States, and Raven Klaasen, South Africa
Jelena Jankovic (8), Serbia, vs. Simona Halep (11), Romania
Ashleigh Barty and John Peers, Australia, vs. Katarina Srebotnik, Slovenia, and Rohan Bopanna (2), India
Andy Murray (4), Britain, vs. Stephane Robert, France
- AAP