After blasting her way through the first set without losing a game, Boulter was pegged back but dug in impressively, coming from a break down to reach 6-6 in the deciding set.
A change in the rules for this tournament means matches that reach that stage will be decided by a first-to-10-points tie-break, and Boulter was the first player to win such a contest, coming through 6-0 4-6 7-6 (10/6) after two hours and 24 minutes in oppressive Melbourne heat.
Boulter thought she had won the match when the score reached 7-4, which would have been the end of a conventional tie-break, but recomposed herself to finish off the job.
Makarova is a two-time grand slam semi-finalist, including here four years ago, and can boast 13 wins over top-10 players at the slams but Boulter crashed 53 winners past her and showed superb fighting spirit.
The 22-year-old from Leicestershire might have won it in straight sets but lost eight straight points from 4-4 0-30 in the second set and then found herself 1-3 down in the third.
She responded straight away, her flat forehand doing most of the damage, and put a lot pressure on Makarova but could only take five of the 17 break points she created.
Boulter next faces 11th seed Aryna Sabalenka, who is among the favourites to win the title.
It was not such a happy start to the tournament for Heather Watson and Harriet Dart, who was handed the dreaded double bagel in a 6-0 6-0 loss to childhood idol Maria Sharapova on Rod Laver Arena.
Dart's under-powered serve took a pounding at the hands of the Russian, the champion here 11 years ago, and the young British player was left in tears afterwards.
The 22-year-old, who came through three matches of qualifying for the first time at a slam, said: "It was always going to be a difficult match, especially on such a big court. She's got a lot more experience than me but I came through qualifying so that's something to be positive about.
"I think I carried myself well out there, played all right, won more points than I thought I'd won. Just unfortunate not to get on the board but this happens. Next time I'll be a bit more prepared."
The unwanted record of first player out of the tournament actually fell to Watson, whose disappointing form continued with a 6-1 6-2 loss to 31st seed Petra Martic.