Sydney-born Sweeny secured the spot on Thursday, winning his third straight match in qualifying at Melbourne Park, and was followed up by former doubles world No.1 Hunter, who downed American Taylor Townsend.
Cheered on by a court packed with vocal home fans, 24-year-old Sweeny overcame Italy's Stefano Travaglia 7-6 (7-5) 7-6 (7-3) to qualify for the Open for just the second time, following his 2024 campaign.
Sweeny made a first-round exit at what was his only previous appearance at a major, and is currently ranked No.182 in the world.
After Thursday's win, an emotional Sweeny sat court-side with his head in his hands, soaking up his achievement.
"I'm in disbelief," he said.
"Really, I was ranked 700 not so long ago, and I persevered, I was doubting the whole time.
"I just feel so incredibly grateful to be able to be in this position, and I'm proud of myself for digging in there when it was really tough.
"So I can't really believe it yet, but I'm super excited."
The diminutive Sydneysider, who only weighs 63kg and stands 170cm, threw himself into every point in a stunning acrobatic display that often ended with him splayed across the court.
It appeared he had injured his wrist in the second set while diving for a shot, but he shook it off and played on.
"I don't even have a decision when I do that, it's just intuitive, it just happens," Sweeny said.
"I think it just comes from being small and learning to scrap from a young age."
On the back of her 7-6 (8-6) 6-2 victory, Hunter is looking to repeat her 2024 Open performance, when she won through qualifying and then advanced through to the third round.
The 31-year-old ruptured her Achilles a few months later in April 2024 and has been on the comeback trail since.
Hunter served for the first set but Townsend, also a former doubles world No.1, pounded a backhand winner and then levelled at 6-6 before the Australian took the tie-break 8-6.
Hunter broke her 11th-seeded rival and then went up 4-2, and with three match points, sealed the win with an ace.
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