Australia took a 2-0 lead with wins in both Friday's singles matches against Taiwan at the Asia-Oceania group one Davis Cup tie in the southern Taiwanese city of Kaohsiung.
Following the day's loss, Taiwan must win in Saturday's doubles to avoid a crushing defeat.
Matthew Ebden picked up his team's second point of the day with a 6-3, 6-4, 7-5 win over Chen Ti, rewarding Australian captain Pat Rafter's decision to pick him for the singles over team-mate Marinko Matosevic.
Lleyton Hewitt had earlier delivered an efficient 6-4, 6-4, 6-4 win over Yang Tsung-hua, which marked the Australian's 39th singles win in Davis Cup play.
Hewitt needed all of his experience to overcome Yang, supported by an enthusiastic home crowd, and give Rafter and the small but noisy contingent of travelling fans reason to cheer.
It was Yang who appeared to struggle more in the hot and humid conditions, and he needed treatment after the second set for what appeared to be a back problem.
Hewitt, who turns 32 later this month, showed few signs of the foot problems which dogged him for much of the 2012 season.
Rafter has hinted that he may also change the Australian line-up for Sunday's reverse singles if needed.
Hewitt has been chosen to play in Saturday's doubles alongside Chris Guccione against Taiwan's Lee Hsin-han and Peng Hsien-yin.