The Japanese third seed, who won the second of her three Grand Slam titles at Melbourne Park in 2019, beat the Taiwanese 6-2 6-2.
Osaka will face either Serena Williams or Simona Halep – who are both former Grand Slam champions – for a place in Saturday’s final.
“Every time I play her, it is always such a battle,” Osaka said.
Osaka has had a difficult draw but the 23-year-old has dropped just one set en route to the last four.
She saved two match points to beat two-time major winner Garbine Muguruza in the quarter-finals and looked refreshed against Hseih.
After saving a break point in the opening game of the match, Osaka chased down Hseih’s slices and shots to take an early break in the first set.
She hit 24 winners, compared to 14 unforced errors, and amassed 12 break points on the Hseih serve, converting four.
Osaka beat Williams to win her maiden Grand Slam title at the US Open in 2018, but she has won just one of her previous four matches against Halep.
Asked if she would watch the match later on Tuesday, Osaka said: “I always watch Serena’s matches.
“It’s definitely going to be a lot of fun.”