Dellacqua came into the match on some very impressive numbers - she had won 23 of her last 27 matches and risen from outside the Top 100 all the way to No.56 on the latest rankings, on the verge of making the Top 50 for the first time in more than five years. Needless to say, she was dangerous.
And for most of the match it was a toss-up - Williams won the first set, Dellacqua snuck out the second set, and after Williams went up 4-2 in the third, Dellacqua caught up to 4-4. But the No.29-seeded American made one last push to edge the Australian wildcard right at the finish line, 64 57 64.
Awaiting Williams in the next round is No.10 seed Dominika Cibulkova, who was on court almost as long - two hours and 12 minutes - and beat No.22 seed Alizé Cornet in a tight two-setter, 76(6) 64. The first set could have gone either way - Cornet led 5-2 and would eventually miss five set points.
Cibulkova and Williams are tied in their head-to-head, 1-1. They haven't met in almost four years.
"I think since the last time we played I'm a different player, a more experienced player," Cibulkova said. "Right now I'm feeling very cool and confident on the court, and I'm playing well. But she's playing well too - she just won Dubai - and she feels at home here in Miami. It will definitely be a tough one."
"I don't even know the last time I played her, but I know every time she plays Serena she competes so well," Williams said of Cibulkova. "I think they played here last year in the semifinals. I was watching that match. It may have been a three-setter - I just remember the match was really, really tough."
Also setting up a fourth round clash were No.11 seed Caroline Wozniacki and Varvara Lepchenko. Lepchenko was the first to advance, edging Ajla Tomljanovic in a two-hour, 59-minute marathon, 64 67(4) 76(2), and Wozniacki followed with a 61 60 demolition job against No.17 seed Sloane Stephens.
"Honestly, I just kept playing, stopped focusing on the score, and just focused on myself and what I wanted to do out there," Wozniacki said. "Things can turn easily, especially when you're up by a lot, and the other player has nothing to lose, so you have to be on your toes and expect anything.
"I stayed focused. I didn't let her in. I didn't give one point away. I was very happy about that."
Stephens didn't beat around the bush. "Just got my butt kicked, that's about it really," she said. "I tried a lot of things, and it just wasn't my night. It was disappointing. Just didn't click for me."