Finishing 2023 ranked world No.1 in doubles, Hunter is also chasing singles success at Melbourne Park and faced a tough first round qualifying opponent in Kanepi.
The Estonian 38-year-old is an accomplished eight-times grand slam quarter-finalist and most recently made the last eight in Melbourne in 2022.
Kanepi took out former champion Angeiique Kerber and now reigning title holder Aryna Sabalenka in a giant-killing run before falling to world No.1 Iga Swiatek in three sets.
But the part-time truck driver was no match on Wednesday for in-form Hunter, who secured a comfortable 6-3 6-2 victory.
Hunter, 29, trailed 0-3 in the first set but settled into the match and reeled off six straight games.
The pair traded early breaks in the second before Hunter steamed away for the win.
Hunter, who played doubles in Australia's run to last week's United Cup semi-finals, said it took a few games to get her head in the match.
She said she felt she had the game plan to topple Kanepi despite the early hiccup.
"Kaia is an unreal player - I played her last year and lost pretty convincingly but I knew her game and felt if I could just get on the front foot I could cause some damage," Hunter told AAP.
"I'm just really proud of myself how I kind of came back from starting pretty average to compete and enjoy it and it ended up being a good match."
Currently ranked 175th, Kanepi has been ranked as high as world No.15 with Hunter wary of her grand slam history.
"She's obviously gone deep in slams so I was surprised I drew her in the first round," she said.
"It was definitely not an easy first match-up and I had to bring it from the first point and it's actually a really good match to get through today."
In other early first-round featuring Australians, 17-year-old Maya Joint ground out 6-3 1-6 7-5 win over Serbian veteran Natalija Stevanovic.
Omar Jasika, who won the US Open boys singles and doubles titles in 2014, moved through to the second round with a 6-3 1-6 6-2 win over Czech Dalibor Svrcina, who suffered a hamstring injury late in the match.
The Australian hasn't made the main draw of a grand slam since 2017, with his career stalled in 2018 by a two-year drug ban after testing positive for cocaine.
Ranked 341st, Jasika is hoping to make the most of another chance.
"I've grown up and matured a lot  and I'm so happy to be back here," the 26-year-old said.
"It's always great to be back playing in front of friends and family who helped me so much over the last few years."
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