The 22-year-old from Penrith, having qualified for his first main-draw appearance at an ATP Masters event, took no time in enjoying his first triumph at this exalted level, beating Japan's world No.96 Taro Daniel 6-2 6-3.
He's one of 11 Australian men who made it into the opening round of the ATP 1000 event, one of the biggest tournaments outside the grand slams, with three winning their opening matches on Wednesday to make it into the last 64.
It was the first time Sweeny, ranked 256 in the world, had earned a scalp in the ATP's top 100, and he did so in the most efficient manner, converting four of five break point chances against the experienced Florida-based Daniel.
It will get no easier for Sweeny as he faces the world No.27 Sebastian Baez, from Argentina, in the next round.
He was not the only Australian to progress, with Thanasi Kokkinakis, who impressed during his national team's recent Davis Cup group stage success in Manchester, left delighted as he outplayed Italian veteran wildcard Fabio Fognini 6-2 6-4.
His serve remained unbroken throughout the 79-minute clash, with the Adelaide player rating his first set as one of the best he could ever recall playing. "A pretty polished performance," he called it.
The first two Aussies in the main draw to get knocked out were James Duckworth and Max Purcell.
Duckworth battled for all he was worth against German Yannick Hanfmann, saving four match points in the second set tiebreaker before forcing a decider and then saving a fifth before finally being beaten 6-4 6-7 (10-12) 6-3 after just under two-and-a-half hours.
There was a big disappointment too for Duckworth's fellow Sydneysider Purcell, who went down 7-6 (7-5) 4-6 6-4 to Taiwan's Yu Hsiou Hsu, ranked 140 places lower than the Sydneysider on the ATP computer.
Sweeny's progress echoes that of Philip Sekulic, who has also battled through qualifying in Shanghai after his own breakthrough week at the China Open in Beijing, where the 20-year-old from Subiaco also earned his first tour-level win.
Facing Italian Lorenzo Sonego, Sekulic will be one of six more Australians in action on Thursday, along with Rinky Hijikata, Alexei Popyrin, Aleksandar Vukic, Jordan Thompson and Chris O'Connell.
Also in the opening round in Shanghai, two grand slam greats bit the dust, Andy Murray being defeated 6-3 6-2 by Russian Roman Safiullin, while Stan Wawrinka was tamed 6-4 7-6 (9-7) by Serbian Dusan Lajovic.
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