The 22-year-old Londoner continued her fine start to the season by recovering from a set down to beat 10th seed Ivana Jorovic 1-6 6-3 6-1 while Dan Evans made it eight British players in the main singles draws with a 6-3 6-3 victory over Paolo Lorenzi.
Dart, who grew up idolising Sharapova, said: "I'm super excited and happy. I've been playing good tennis and I've put a lot of hard work and effort into all my training, my pre-season, so I knew my level was there, it was just about piecing it all together.
"She came out of the blocks early very good. I managed to stay in there and found a way to win. That's what I'm really proud of today."
Dart only made her slam debut as a wild card at Wimbledon last year - taking a set off Karolina Pliskova - but for Evans this is familiar territory.
The 28-year-old reached the fourth round on his last appearance at Melbourne Park in 2017 but will play in the main draw of a slam for the first time since his 12-month drugs ban.
He returned last April at a low-key Challenger in Glasgow and is already back in the world's top 200, with the carrot of a second-round clash against Roger Federer if he can get past fellow qualifier Tatsuma Ito.
Evans said: "I'm happy. Obviously I knew when I got banned I would have to start at not a great tournament and hopefully make my way back up. I'm nowhere near where I want to be yet so it's just another step in the right direction."
There was no repeat of the remarkable winner Evans played from behind his back in his second-round win over Jurij Rodionov that has already been hailed as the shot of the year.
He agreed it was the best shot of his career, but added: "It was obviously very lucky. I just stuck my racket out basically and it went in."
