Showing plenty of the never-say-die traits of his doppelganger Lleyton Hewitt, the world No.257 traded blows for the best part of three and half hours on Sunday before bowing out 3-6 6-3 6-4 2-6-6-2.
Cerundolo dominated the winners' count 57-20 but the 22-year-old Sweeny's counter-punching qualities kept him in the contest throughout.
The seeded Francisco Cerundolo had to work hard for his win against Dane Sweeny. (James Ross/AAP PHOTOS)
Countryman and wildcard recipient Adam Walton made an encouraging start on his major debut before being overwhelmed by rising Italian star Matteo Arnaldi.
Playing just his second Tour-level match, the 24-year-old Walton served for the opening set at 6-5 on Sunday but was unable to hold.
World No.41 Arnaldi took command in the tiebreak and then put his foot down to win 7-6 (7-5) 6-2 6-4.
The 22-year-old Arnaldi was a member of the victorious Italian Davis Cup team in 2023, beating Australia's Alexei Popyrin in the opening match of the final.
He also reached the fourth round of last year's US Open before losing to Carlos Alcaraz.
Adam Walton started well before succumbing to Italian star Matteo Arnaldi. (James Ross/AAP PHOTOS)
Walton cut his teeth on the US college circuit from 2017-22 with the University of Tennessee, winning the 2021 NCAA doubles title.
He and Sweeny are among the 15 Australian men in the singles draw at Melbourne Park this year, the largest local contingent since 1998.
Compatriots Chris O'Connell and Jason Kubler get their campaigns underway later on Sunday.Â
Australia's highest-ranked player, No.10 seed Alex de Minaur, has been handed a difficult first-round clash with 2016 Wimbledon finalist Milos Raonic on Monday night on Rod Laver Arena.
The big-serving Canadian has endured a wretched two-year run with injury but still shapes as a dangerous floater.
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