Williams, widely condemned for her rant at a line judge at the US Open in 2009 - which cost her the point and, as she was defending match point, the match - is known for her explosive temper. But it doesn't often come out as she wins far more tennis matches than she loses.
However we were given a sudden reminder in perhaps the least appropriate circumstances against Stephens: Serena has been something of a mentor in the 19-year-old star's fledgling career, and Stephens is often cited as a potential successor to the multiple Grand Slam-winning queen of tennis.
Stephens was genuinely excited to be playing her hero in the last eight - she had a picture of her on her bedroom wall while growing up - and put in the performance of an established Slam champion in the third set to make the most of Williams's back problem.
That was picked up at the end of the second set and resulted in Serena smashing her racquet repeatedly into the floor then flinging it away courtside in disgust as the teenager glided to her own chair.
"I've seen her do it before but this is tennis, it happens. She's still going to play, smashed racquet or not. You're playing Serena, one of the best competitors in the world. Now you're going to have to play harder," said an unperturbed Stephens afterwards.
Before the match Serena understandably refused to take responsibility for anything to do with her compatriot's career. "No. I feel no responsibility. I doubt she has any expectations of me to be responsible for anything. Maybe she does. I don't know... Maybe some of the younger players look up to me. It's interesting. It's hard to be a real mentor when you're still in competition."
That was evident in her outburst, which can hardly be described as becoming of a Grand Slam champion, never mind a mentor. Can you imagine Roger Federer embarking on such a racquet rampage?
Without wishing to preach about 'setting an example to the kids', Tramlines is going to do exactly that: there is a correct way to lose, and all too often Serena shows herself unaware of this.
Two years after that 2009 controversy - where she allegedly told the line judge she was going to force a ball down her throat if she called another foot fault - she ranted at the umpire of her losing final against Sam Stosur.
Having yelled 'come on!' before a winner to the corner was out of play, the point was awarded to the Australian - and the following tirade has gone down in folklore.
"Aren’t you the one who screwed me over here last time?" - this was not the case - "I truly despise you. If you ever see me walking down the hall look the other way. You’re a hater, and you’re just unattractive inside. And I never complain. Wow, what a loser."
The third-set heroics of Stephens - who joked afterwards that she will have to put a poster of herself on her bedroom wall now - are what this match should be remembered for, not the childish tantrum of tennis royalty.