Konta was followed into the quarter-finals by men's world number two Andy Murray, who beat Australian Bernard Tomic 6-4 6-4 7-6(4), to give Britain their first man and woman in the last eight at a grand slam in almost 40 years.
Sue Barker, Robin Drysdale and John Lloyd reached the Australian Open quarter-finals in 1977.
Konta is the first British woman in the last eight at Melbourne since Jo Durie in 1983.
Although she wobbled while serving for the set at 5-4 in the decider, she made no mistake at the second opportunity after three hours, four minutes of graft in Margaret Court Arena and threw her arms skyward in jubilant relief.
"I really enjoyed the match for what it was," she said. "It was a very high-level match against a very, very good player.
"It was definitely one of the more spectacular matches I've played."
Sydney-born Konta, who became a British citizen in 2012, said she had held up well physically after the marathon clash with Makarova and while she joked she was going out to enjoy the Melbourne night life, her immediate plans involved going to bed.
"I actually feel, knock on wood, pretty good," the 24-year-old said.
"It's a very emotionally charged situation to be in.
"I'm going straight back to bed. I'm really looking forward to it."
She will meet either Zhang Shuai or Madison Keys in the last eight.
"We're talking about a quarter-final of a grand slam, so whoever I'm going to play it's going to be an incredibly good player," she added.
(Reporting by Ian Ransom and Greg Stutchbury; Editing by Ed Osmond)
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