Top-seeded Federer dropped only six points in a 16-minute first set, and won 6-0, 6-1 without really breaking a sweat against No. 125-ranked Duckworth — a vast contrast to his rusty, three-set opening win over John Millman the previous night.
"I had a great start to the match," Federer said. "I saved energy and stress and nerves.
"Yesterday was quite nerve-wracking and physically difficult because it was first match of the season. So I'm very happy I got it done quickly today."
The 17-time major winner will next meet No. 4-seeded Grigor Dimitrov, who advanced a 6-3, 6-4 winner over Martin Klizan of Slovakia.
No. 2-seeded Kei Nishikori and No. 3 Milos Raonic, of Thornhill, Ont., will meet in the other semifinal after beating Australians.
The top two players in the women's draw will meet in the final after No. 1-seeded Maria Sharapova beat Elina Svitolina 6-1, 6-3, and No. 2 Ana Ivanovic had a 7-6 (2), 6-4 win over Varvara Lepchenko.
Federer and Dimitrov are often compared due to their styles, particularly the single-handed backhand, and they're both anticipating a great semifinal.
"I'm aware of the challenge," Federer said. "He's clearly expecting big things from himself this year, I would assume.
"So, it's an opportunity for him more than for me, but I still think it's going to be a tough and good match for both of us."
Dimitrov has lost two previous matches to Federer — both at Basel — but is growing in confidence after rising to a career-high No. 8 ranking last August.
"I'm always excited when I get to play a match like that against a player like that," Dimitrov said. "I have quite a bit of experience behind me now. I've learned from each match that I've played against him. I like my odds."
Nishikori, the U.S. Open finalist, breezed past Bernard Tomic 6-0, 6-4, while Raonic had more of a struggle against big-serving Sam Groth, winning 7-6 (3), 3-6, 7-6 (2).
Groth got the only break of serve, in the second set, and had more winners and more aces — 22 against 15 — than Raonic, who is rarely outperformed in that area.
Nishikori, Raonic and Dimitrov have yet to win a major title, but they're widely considered the new wave of future champions. They're all playing their first tournaments of the season in Brisbane, getting primed for the Australian Open beginning on Jan. 19.
In the night cap, Sharapova wasted four match points in the eighth game of the second set before dropping serve, but converted her fifth match point in the next game to see off Svitolina.
Ivanovic had some wobbles, too, after leading Lepchenko 5-1 in the second set and needing seven match points before she finally finished it off on her serve.
"I knew she was going to go for it because she had her back against the wall and she was going to go big," Ivanovic said. "I was really happy to stay calm and save break point and then win that (last) game."
Poland advanced to the Hopman Cup final in Perth by clinching a point against defending champion France, setting up a final against the United States.
Alize Cornet beat Agnieszka Radwanska 6-2, 2-6, 7-5 to give France the lead, but Poland secured top spot in the group when Jerzy Janowicz beat Benoit Paire 6-4, 7-6 (6).
At the ASB Classic in Auckland, New Zealand, top-seeded Caroline Wozniacki beat Barbora Zahlavova Strycova 4-6, 6-3, 6-4 in a 2-hour, 35-minute match to set up a final against Venus Williams, who brushed past American compatriot Lauren Davis 6-0, 6-3. Williams also reached the final last year, losing in three sets to Ivanovic.
AP Sports Writer Steve McMorran in New Zealand contributed.