The 25-year-old ninth seed, Britain's last hope of a singles title after Andy Murray and Dan Evans were bundled out on Sunday, took 69 minutes to send her Russian opponent packing in temperatures approaching 35 degrees Celsius.
It secured her a first meeting with 22-times grand slam champion Williams, who won the first of her six Melbourne Park crowns when Konta was an 11-year-old growing up in the Sydney suburbs.
"She's one of the players still playing who I looked up to as a young girl wanting to be a professional tennis player," said Konta.
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"It's an incredible honour and I will cherish every moment out there."
It was with her run to the semi-finals as world number 47 at Melbourne Park last year that Konta first gave notice that she had the game to take on the best in the world.
Extensive work with a sports psychologist had helped Konta rid her game of the mental collapses in big moments that marred the early years of her career and on Monday she explained how she was now able to cope.
"When you get to a position where you might see a glimmer of what you have dreamed of as a little girl or what you hoped for, what you've worked so hard for, it can feel kind of an all-or-nothing moment or, 'What if I never get this chance again?'" she told reporters.
"You have also got to have a good perspective on things, and you've got to keep, I guess, the simple things in mind of what's important to you.
"Are you healthy? Is your family healthy? Do you have people around you that you love? Do you have people around you that love you?
"I know it might sound really mundane and simple, but you've got to go back to things that have got substance, and then in the end just trust in the work that you do."
Konta has shown enormous mental fortitude in reaching the last eight without dropping a set after demolishing the hopes of Denmark's Caroline Wozniacki, Japan's Naomi Osaka and Belgium's Kirsten Flipkens.
On Monday, Makarova was no match for Konta's serve or ground game in the first set as she changed angles and depth of returns that prevented the lefthander from getting any rhythm.
The Russian, who beat sixth seed Dominika Cibulkova in the third round, raced to a 4-1 lead in the second set but Konta rallied to win the next five games.
Konta sealed victory on her second match point when the Russian's forehand sailed over the baseline to move into the quarter-finals as a serious title contender.
Her next match will be the stiffest test yet of those credentials.
"I believe in my own ability," said Konta. "I believe in the good things that I bring to the court, and I believe in my ability to fight till the very end."
(Editing by Amlan Chakraborty)
