The world number one had become the first of the top four seeds to drop a set at Melbourne Park this year in the third round against an injury-hampered Jamie Hampton and said she needed to improve "everything" against Vesnina.
Improve she did, blasting the Russian doubles specialist off court to claim victory in 56 minutes.
"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."
Vesnina won her first WTA Tour title in Hobart before the tournament began, but offered little against the tall right-hander and was simply ground down by the more powerful Belarusian.
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 double Grand Slam winner Sveltana Kuznetsova in the last eight.
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 rejoin 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."
Kuznetsova, unseeded and unheralded after being sidelined for half of 2012, announced her return to the big time in some style with the victory.
The Russian ended a streak of 40 consecutive Grand Slam appearances stretching back a decade when she pulled out of last year's US Open because of a knee injury, but she was back at her battling best to reach the last eight at Melbourne.
Her Major titles and a career high ranking of second in the world bear witness to a big tennis talent but along with those successes there was always a maddening inconsistency.
Both were on display in the centre court win over former world number one Wozniacki as she mixed 52 winners with 41 unforced errors, the latter often coming off miscued forehands.
Still, she prevailed in a highly competitive 75-minute third set to move into the last eight and an appointment with Azarenka.
Despite missing the entire second half of the season after Wimbledon because of the injury, she never doubted she would back and only the speed of her return to the big stage has surprised her.
"If you had asked me before coming to Australia I would have laughed, definitely, and I wouldn't have been so sure about it," the 27-year-old said.
"I have been working hard, but still I didn't have much time to do what I like to do with my fitness and everything else.
"It's amazing. It's a very good result for a first grand slam, and especially as I don't remember when I was last in the quarters."
Her last trip to the quarter-finals at Melbourne Park was in fact in 2009, when she lost to eventual champion Serena Williams.
A few months later she won her second Grand Slam title at Roland Garros to add to her 2004 US Open crown, and she finished that year as world number three.
Her slide down the rankings to her current 75th in the world started long before her injury, however.
Despite the slump, she said she never really considered calling time on tennis even if a long rest for the first time in her career was welcome.
"I never had a thought of stopping tennis," she said. "I was just laying in bed, and I was like, thanks my knee. At least I can rest.
"When the knee was sore it was so annoying to walk with the crutches all day long. I went to Thailand, I went to Bali, on the beach with crutches, all day long, and I had blisters on my hands.
"This was the most annoying thing, and then recovery. But anyway, I had time at home to just refresh my mind, and then I just understood that I wanted to play this game.
"I mean, I always loved it, but I wanted to have this desire to bring me back. This is what happened."
After 12 years as a professional Kuznetsova knows what she does best and is confident she can have a good go at improving still further her 4-3 head-to-head record against Azarenka.
"I play good forehand, serve well. To be aggressive, this is my main key. But I keep some secrets for me, not everything for you," she laughed.
"I have nothing to lose, she has all the pressure," she added. "I know I have got the game to give her some problems, and I will just do my best and just try to enjoy it."
Wozniacki was disconsolate after failing to reach the quarter-finals at Melbourne Park for the first time in three years.
"I had my chances and I didn't take them," said the Dane.
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