Baghdatis, a 20-year-old from Cyprus, defeated Roddick, the 2003 U.S. Open champ and two-time Wimbledon runner-up, 6-4, 1-6, 6-3, 6-4 at the first Grand Slam tennis event of the season.
The big-hitting Roddick was seeking his third trip to the Australian Open semifinals in four years.
With defending champion Marat Safin of Russia, second-ranked Rafael Nadal of Spain, four-time winner Andre Agassi of the U.S. out because of injuries and No. 3 Lleyton Hewitt of Australia eliminated in the second round, Roddick was considered the top contender to challenge favourite Roger Federer of Switzerland.
In other play Sunday, fourth-seeded Argentine David Nalbandian handled 16th-seeded Spaniard Tommy Robredo 6-3, 6-0, 2-6, 6-2.
Veteran Frenchman Fabrice Santoro smoked 11th-seeded Spaniard David Ferrer in straight sets 6-4, 7-5, 7-5. Ferrer will meet Nalbandian in the next round. One other bout will pit seventh-seeded Croat Ivan Ljubicic against 10th-seeded Swede Thomas Johansson, the 2002 Australian Open champion.
The winner will battle Baghdatis in the next round.
Federer will play Tommy Haas of Germany, who beat him in the 2002 Australian Open and at a pre-tournament exhibition match last week.
"I'm really looking forward to that match," said Federer.
In women's play, world No. 1 American Lindsay Davenport battled an ankle injury, but still managed to breeze past Russian Svetlana Kuznetsova in fourth-round play.
Davenport, last year's Australian and Wimbledon runner-up, sent the 14th-seeded Kuznetsova packing with a 6-2, 6-4 triumph. The 2000 Australian Open champion, Davenport has not won a major since her victory Down Under.
She had to seek medical attention on her left ankle in the second set, but she brushed off the pain and a few unforced errors and finished off her Russian opponent.
"I sprained it a little bit the other day," said Davenport. "It was just a little bit swollen ... I kind of jammed it on one shot. Hopefully, it will have a little time to get better."
Davenport, a three-time Grand Slam winner, will take on the eighth-seeded former world No. 1 Justine Henin-Hardenne of Belgium.
Henin-Hardenne, who won this prestigious title in 2004, defeated Spanish doubles specialist Virginia Ruano Pascual 6-0, 6-3.
The four-time Grand Slam champion and former world No. 1 Henin-Hardenne has now won her last 11 matches Down Under, having missed the event last year due to injury.
Sixth-seeded Nadia Petrova toppled fellow Russian Elena Vesnina by a 6-3, 6-1 score and will face the winner of the Maria Sharapova/Daniela Hantuchova matchup in the quarter-finals.
The Russian Sharapova, seeded fourth, will take on the 17th-seeded Hantuchova of Slovakia later in the fourth round.
Hantuchova beat 2005 champion Serena Williams in the third round.
Heat forced organizers to enforce the extreme heat policy for the third straight day, suspending play on outside courts when the temperature exceeded 36 C before noon. All fourth-round singles matches were scheduled under closed roofs at the two arenas.
The forecast expected the temperature to rise to 41 C.
with files from Associated Press and Sports Network
