Djokovic, who has been troubled by an elbow injury, crushed Donald Young 6-1, 6-2, 6-4, while Wawrinka, who had knee surgery last summer, recovered from a mid-match slump to beat Ricardas Berankis 6-3, 6-4, 2-6, 7-6.
The Swiss maestro won 6-3, 6-4, 6-3 on Rod Laver Arena to kick off his title defence in style, hinting at a possible repeat of last season's remarkable exploits that saw him add Wimbledon success to his Melbourne triumph.
But Djokovic, a six-time champion in Melbourne, insists the reports have been "taken out of context".
The win was a relief for Djokovic, who says he's still not 100 percent after six months off the tour with an injured right elbow and who lost in a second-round shocker here previous year.
His trickiest adversary might have been a cringe-worthy post-match engagement with actor Will Ferrell.
But still Sevastova was not done and broke back again to force a tiebreak.
It was the Latvian 14th seed who ended her Grand Slam comeback in the last 16 of the US Open in 2017 as she returned from a drug ban.
The British hope Johanna Konta's love affair with the Australian Open came to an abrupt end when she was defeated by the American Bernarda Pera.
Sixth seed Karolina Pliskova stormed past Brazil's Beatriz Haddad Maia, winning 6-1 6-1 in 44 minutes, and next will play fellow Czech Lucie Safarova, who beat Romanian Sorana Cirstea 6-2 6-4.More news: Iranian, Russian FMs Discuss Syria, JCPOA
Top-ranked Simona Halep had to save set points at 5-2 down in the first set, and badly twisted her left ankle early in the second, before beating teenage wild-card entry Destanee Aiava 7-6 (5), 6-1.
The fifth seed, Dominic Thiem of Austria faced Guido Pella of Argentina.
Ninth-seeded Johanna Konta was more exposed to the heat on an outside court, and lost to US lucky loser Bernarda Pera 6-4, 7-5.
Stanford alum Nicole Gibbs beat Viktoriya Tomova 6-1, 6-1.
Muguruza had little to celebrate in a 7-6 (1), 6-4 loss to No. 88-ranked Hsieh Su-wei, who has been No. 1 in doubles but had only previously beaten one top 10 player in singles.
German Andrea Petkovic won the final three games to beat two-time Wimbledon victor Petra Kvitova 6-3 4-6 10-8 in a thrilling first-round encounter, which lasted two hours and 52 minutes. Monfils' only win over Djokovic came in challenger play in 2004, their first meeting.
Bernarda Pera, a Croatian-born American who lives in New Jersey, beat Anna Blinkova of Russian Federation 6-2, 6-2 for her first win at a Grand Slam.
The jolt to the Sharapova juggernaut was evident and she began to make unforced errors as service holds and breaks were exchanged. She got a lot of help from a badly misfiring Sharapova that day in NY, the kind of help you can't count on getting again from a five-time Grand Slam champ.