Jack Draper opened with an impressive straight-set win over Sebastian Baez at the Adelaide International but fellow Briton Katie Boulter lost.
Draper, 22, comfortably beat the 26th-ranked Baez 6-1 6-3 as he continues his preparations for the Australian Open.
However, British number one Boulter suffered a 6-3 6-4 defeat by Romania’s Anna Bogdan in the women’s event.
Qualifying for the Australian Open was set to begin on Monday but rain prevented any matches being played.
The Australian Open, the first Grand Slam of the year, starts in Melbourne on 14 January.
Draper, the world number 62, is set to join Boulter, Jodie Burrage, Emma Raducanu, Cameron Norrie, Dan Evans and Andy Murray in the main draw in Melbourne.
Following a breakthrough 2022 in which he reached a new career-high ranking 22 times, Draper made his debut appearance at the tournament last year but struggled with cramp as he lost to Rafael Nadal in four sets in the opening round.
Contesting his first match of the year following a 2023 season disrupted by a shoulder injury, a fit and firing Draper always looked in control against 23-year-old Baez.
He closed out the opening set by winning five games in a row before another double break of serve settled the second after one hour and 18 minutes.
“I’m very happy with my performance today. It’s not easy coming out for the first match of the year,” said Draper, who will play Miomir Kecmanovic or Mackenzie McDonald in the second round.
“I feel really confident, really happy with my body and my game. I just want to carry on playing injury-free.”
World number 57 Boulter, 27, will now turn her attention to the Australian Open following her exit against 66th-ranked Bogdan.
Both players resisted break points in the early stages but Bogdan, 31, was able to serve out the first set after making the breakthrough in the eighth game.
And although Boulter took a 2-0 lead at the start of the second, Bogdan battled back – with a run of four consecutive games putting her on course for victory.
Brits ready for action after Australian Open qualifying delayed
Harriet Dart and Heather Watson are among eight British players who will be aiming to join their compatriots in the Australian Open main draw once qualifying is able to get under way.
However, Liam Broady will not compete, with the 30-year-old withdrawing from qualifying after an MRI scan revealed two bone stresses in his ankle.
Following adverse weather, Monday’s matches were rescheduled for Tuesday, which is forecast to be sunny and dry.
All eight British hopefuls, who must progress through three qualifying rounds to reach the main draw, are scheduled to play tomorrow.
British number three Dart faces Italy’s Nuria Brancaccio and Watson takes on Swiss player Lulu Sun.
Also in the women’s draw, Yuriko Miyazaki meets Australian teenager Melisa Ercan, while Francesca Jones comes up against Margaux Rouvroy of France.
The men’s draw sees Jan Choinski begins his campaign against Lebanese player Benjamin Hassan, with Ryan Peniston playing Sweden’s Elias Ymer.
Bulgarian Dimitar Kuzmanov is first up for Billy Harris and Oliver Crawford, who recently switched from representing the United States, faces Belarusian Ilya Ivashka.
