On Sunday, the Belarusian was once again second best when they met in the final of the Brisbane International, Williams bouncing back from two dropped service games in the second set for a 6-4, 7-5 victory.
It marked a 14th win for the American in the 17 encounters between the top two in the women’s game and, for her part, Azarenka is not ashamed to admit there are times she wishes one of the game’s greatest players had hung up her racket some time ago.
In 2012, Williams defeated Azarenka in a Wimbledon semi-final and then repeated the feat on the same hallowed turf just a few weeks later to deny her rival a shot at Olympic gold.
Also that year, Azarenka had been on the cusp of winning the US Open, serving 5-4 up in the final set only to be undone by Williams, as she was again in the final at Flushing Meadows last year.
So it is not surprising that the 24-year-old says: “Sometimes, it would have been better for my CV if she wasn’t there but, hey, that’s the way it is and I also like her and respect her very much.
“She’s always the one to beat… and it is always good to have someone to look at so that you keep improving and I take it like that.”
Williams, who Azarenka has previously described as “the greatest of all time”, started this year with the seeming invincibility she ended 2013, in which she won 11 tournaments and 78 out of her 82 matches in all.
In Brisbane, she did not drop a set and looks in ominous form for when the Australian Open begins in Melbourne on Monday.
But 2013 proved something of a turning point for Azarenka, too. In Qatar at the start of the year, she defeated Williams for the first time since 2009, a feat she repeated later in the year in Cincinnati in one of the matches of the year before being undone in a tight US Open Final.
Azarenka admits she has relished those encounters.
Tall order: Winter has been spent in Hawaii, LA and Europe, trying to figure out how to create the downfall of Williams (pictured)Asked if Williams brings out the best in her, she admits: “I think so. I always try to play my best but definitely those two matches [in Cincinnati and New York] were special.
“I feel I played good at both but only managed to win in Cincinnati.”
While Williams is confident in Melbourne so too is Azarenka. This year, she is bidding for a hat-trick of Australian Open women’s singles titles, aiming to emulate the feat last achieved by Martina Hingis in her pomp in 1999.
“I have played some of my best tennis there and the people are great,” she says. “It’s one of those events I always enjoy playing.
“Australia is a country I love and always enjoy being there. The whole atmosphere... I just love it so much. And, yes, I have had some great results in the past two years there.”
Last year’s victory was not without problems, in particular her semi-final win over Sloane Stephens when she took a controversial 10-minute medical time-out while 6-1, 5-4 up, citing breathing problems after squandering five match points.
That led to accusations of gamesmanship, while in the final against Li Na she was jeered by many in the crowd but overcame that to win in three sets — 4-6, 6-4, 6-3.
Looking back at that and the prospect of more boos this time around, Azarenka says: “For me, it is forgotten and I keep the memories of all those other days I have been in Australia with the great people there. And, of course, the memories of the final.”
Winter has been spent in Hawaii, Los Angeles and Europe, plotting how to more consistently create Williams’s on-court downfall. Such were the sacrifices in that quest, Christmas Day even became secondary to tennis.
“This year I was on a plane the whole of Christmas Day so there wasn’t really a celebration,” she says.
The main focus, by her own admission, over the season break has been on her “fitness condition to play the game”. She began the year feeling fresh, which was in part down to an unwarranted break last summer when she tumbled out of Wimbledon following a knee injury.
Unsurprisingly, Azarenka would have preferred to not get injured and have less time out of competition but believes the break “went well”.
One wonders what she might have achieved for the rest of 2013 without the injury, how much closer she may have got to Williams at Flushing Meadows, in particular.
“Unfortunately, I got injured at Wimbledon where I thought I was playing great at that point of the season,” she insists. “There’s not much I can do now about 2013 so I am only focusing on 2014 and hoping to improve my record this year.”
She describes last season as an “up and down year” and the quest this time is to have greater consistency and to stay injury free.
Of the opening week of the year so far, she says: “I’m off to a good start. Let’s hope that it continues.”