Halep yet to drop a set this fortnight in Melbourne, the fourth-seeded Halep needed just 53 minutes to ease past Kontaveit 6-1, 6-1, losing a mere 12 points on serve throughout the match.
Garbine Muguruza held her nerve to overcome a self-destructing Anastasia Pavlyuchenkova 7-5 6-3 and reach her first Australian Open semifinal.
Muguruza is a two-time Grand Slam champion, winning the French Open and Wimbledon, but she has never produced her very best on hard courts, previously failing to progress beyond the last eight at either the Australian Open or the US Open. At the start of the tournament, it seemed unlikely she would end that streak this fortnight after a disappointing 2019 which saw her form and ranking nosedive and she arrived in Melbourne unseeded.
"I wasn't thinking that far away," admitted Muguruza. "I came not feeling great. I wasn't really thinking, 'How far will I go? I had enough already thinking, How will I go practice today?' I took every day at a time. Each day I was gaining a better feeling instead of getting frustrated thinking in the future."
That has all changed over the past week-and-a-half as she has swept into the last four with at times spectacular displays of hitting. Since being bagelled in the opening set of her first-round match against Shelly Rogers, Muguruza has reeled off successive top-10 wins over Elina Svitolina and Kiki Bertens.
However, today was arguably her least convincing performance so far. Pavlyuchenkova will leave Melbourne wondering how this one slipped through her fingertips having led by a break in both sets, and yet managed to self-destruct on each occasion.