As for Venus, she attributed the victory to having more match practice than her sister, and credited Serena for her attempted fightback from two breaks down in the second set.
The seven-time major victor defeated Serena for the first time since 2014, while claiming her first straight-sets win against her youngster sister since 2008, despite a late stumble.
Wozniacki, who will face 20th seed Daria Kasatkina for a spot in the quarter-finals, said: "I was struggling finding my rhythm".
Serena had won eight of their previous nine meetings, but Venus managed to dispatch her in a respectable hour-and-a-half, in a match filled with blistering serves and returns from both ends of the court.
Serena didn't expect her instincts would return so quickly, and said Monday that she looks forward to what will ultimately be a quest in getting back to the No. 1 ranking, where she was when she stepped away from the game for 14 months after winning the 2017 Australian Open over Venus.
"I haven't played in over a year; it's definitely not less disappointing, I wish it were, but then again, I wish it wasn't". But then I wouldn't be who I am.
"I just have a long way to go", Serena said.
This is actually Serena's first Tennis appearance since after the birth of her daughter in September and the match against her sister is the 29th one with Venus losing out in four matches in total. I make those shots 10 times out of 10 in practice. It is even possible that, all these years after that infamous 2001 tournament, the oldest woman in the draw could win her first Indian Wells title.
The head-to-head record is 17-12, still in favour of Serena now.
"I really abhor every time we play, but I do enjoy the battle when I'm out there", Serena commented last weekend. Venus will next play against Anastasija Sevastova from Latvia in the fourth. My room for improvement is incredible.
'I probably won't play in the very beginning, in Monaco, ' said Federer, who last played there in 2016. I just want to continue to go forwards.
'So I have just got to keep saying at each tournament that my goal is just to be better than the last. However, Venus is still a great player, coming off of a superb year.
In the third round in Indian Wells, Venus Williams beats Serena Williams in straight sets. "She was asking what she was doing wrong, and I was trying to tell her she was rushing too much", Mouratoglou said. "I'm playing a completely different player, new challenges".
Her stamina appeared to get better as the match progressed, and she won several long points.