The 21-year-old wildcard fired 43 winners as she banked a 6-1 6-3 victory in 76 minutes as main-draw play got under way at Melbourne Park on Sunday.
The performance equalled Gibson's  previous best grand slam result, which was a round-two appearance at the Open last year. She also qualified for Wimbledon, where she lost to Naomi Osaka in her first match.
Compatriot Tristian Schoolkate followed Gibson on to court and was ousted in a tough battle against French 32nd seed Corentin Moutet 6-4 7-6 (7-1) 6-3.
Ranked No.119, Gibson looked headed for a crushing win, one point away from taking a 5-1 lead in the second set.
But world No.62 Blinkova, known for her fighting qualities, clawed her way back into the match to pile the pressure on Gibson to trail 4-3.
The Australian regrouped and fired a backhand winner to break her rival at go up 5-4, then served out in style, with a sweeping forehand icing the victory.
With a career high ranking of No.105 in August, Gibson said she was delighted she could play the match on her terms.
"I knew that this match-up today, I was going to be the more aggressive player out on the court, so I think that was exciting for me to be able to go out there and be in control of most of the points," Gibson said.
"That's really what I want when I look for a game like that, so I'm really happy that I was able to execute my game really well today."
Gibson felt she had the power game to compete against the elite players, and will fancy her chances in the second round against either another Russian in Diana Shnaider or Czech Barbora Krejcikova.
"Over the last year I've been able to play against more of these players who are in the top 100, and I think it's been really great for me to be able to see how much I am able to compete with these players," the Australian said.
"I've learnt a huge amount and the biggest thing is how much damage I can do with my game, so I was able to take confidence from the last year and having some really good results."
Schoolkate took one set off two-time Australian Open champion Jannik Sinner in the second round last year which kick-started a career-best season.
But while Moutet took a medical time-out in the third set for an apparent leg injury, world No.98 Schoolkate couldn't take advantage.
Later on John Cain Arena, Jason Kubler couldn't take his chances in a straight-sets loss to 29th seed Frances Tiafoe.
Kubler, who fought through qualifying to reach the main draw, twice had set points on Tiafoe's serve when up 5-4 in the first set but the impressive American saved both.
Tiafoe belted 53 winners to Kubler's 22 as he wrapped up the match 7-6 (7-4) 6-3 6-2 in two hours and 13 minutes.
