The world number one, who was taken a full three sets by an injury-hampered Jamie Hampton in the third round, had said she needed to improve "everything" before facing Vesnina in the fourth.
Improve she did, blasting the Russian doubles specialist off court to claim a 6-1 6-1 victory in 56 minutes and setting up a last eight encounter against double Grand Slam winner Sveltana Kuznetsova.
"I felt like I was playing pretty good today," Azarenka said. "You know, I was focused and in control from the beginning. That was important for me.
"I feel like I'm improving from match to match. I just want to keep going the same way."
The improvement was noticeable as Vesnina, who won her first WTA Tour singles title in Hobart before the tournament began, offered little against the tall right-hander and was simply ground down by the more powerful Belarusian.
Part of that ruthless demolition could be attributed to the music she was listening to beforehand.
Put simply, Azarenka said if her pre-match music is any good, then she plays good.
"I kind of get in the zone, and that's it," she said. "It just makes me feel good.
"When I feel good inside, I love to go out there and do the best job as I can. So I choose very carefully," she said.
Prior to the Vesnina clash, she had been listening to an as yet un-named and unreleased single mixed by GoonRock, who had co-written a number of songs with the now defunct electronic dance music duo LMFAO.
"I got the new mix, actually new song. It didn't come out yet. So I have a first hearing of it," Azarenka said.
"It's really good, called Sweet Baby, something like that. I came up with the name (but) I don't think it has a title yet.
"It's just an amazing mix. It's a remix of an old song."
LMFAO singer Redfoo has been courtside in Azarenka's player's box throughout the tournament and she added that she had provided "vocals" to one of his new songs.
"It's my grunt," she said with a laugh. "I don't take high key or low key there. It's just natural."
Azarenka, who won her first Grand Slam title at Melbourne Park last year as part of a 26-match unbeaten run to start 2012, may have brushed any rust out of her system but is well aware of the challenge that will arise in the shape of Kuznetsova.
The Russian had earlier overcome 10th seed Caroline Wozniacki 6-2 2-6 7-5 in the first game on Rod Laver Arena and shown that after six months out with a knee injury, she may be poised to re-join the women's elite.
"I think it's going to be very tough match," Azarenka said.
"I can see Sveta came back much fresher, much stronger.
"She knows how to handle big stages, big tournaments. She's a Grand Slam champion.
"It's definitely an exciting match for me to be in. I'm sure it's going to be really tough."
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