Tomljanovic was the first to win through, rallying from a first set blowout and toughing out a 73-minute third set to edge Andrea Petkovic, 06 64 76(1). Though they were both wildcards, and Petkovic is playing just her second WTA event back after missing two and a half months with a knee injury, the victory was still a big one given Petkovic is a former World No.9 - a former semifinalist here too.
"She came out hitting the corners and it took me some time to get used to," Tomljanovic said after the match. "We had a really long first game and I couldn't convert on the break points. It was a pretty slow start for me. In the second set I thought, 'If I'm going to lose, I want to lose the right way.' So I really tried to play better and get into the match more and I fought my way through the second set.
"I had a really great start to the third set, going up 3-0, and I had so many chances to close the set out easier than it was, but it turned into a battle. I think we both played really well at the end."
Her feelings on Miami? "I love this tournament," she beamed. "It's my favorite so far. I love it!"
Muguruza's victory came a little later and it was definitely a big upset - the Spaniard recovered from a mid-second set lapse to take out No.9 seed Caroline Wozniacki in straight sets, 62 64. After storming out to a 62 20 lead, Muguruza watched on as Wozniacki reeled off four of the next five games to lead 4-3 in the third set - but she turned it up again just in time to close out the former World No.1.
By beating the World No.9, Muguruza got her second Top 10 win, having beaten a No.9-ranked Vera Zvonareva in the second round here a year ago. That made her the equal-fastest player ever to beat a Top 10 player, that match with Zvonareva being her second WTA main draw match - Andrea Leand beat a Top 10 player in her second WTA main draw match at the 1981 US Open (Andrea Jaeger).
Elsewhere, Agnieszka Radwanska and Li Na dodged upsets, one of them just barely. The No.5-seeded Li was the first to win, storming out to a 62 41 lead over Varvara Lepchenko then, after Lepchenko won three straight games to catch up to 4-all in the second set, closing out the No.25 seed, 62 64.
"I played really well in the first set," Li said. "The second set was really tough to close out and she really pushed me - she definitely lifted her level and intensity and made me work for it today.
"I'm glad to have won in straight sets. The conditions were tough - it's hot and sticky out there."
The No.4-seeded Radwanska bounced back from a disappointing second set to beat Magdalena Rybarikova, 76(5) 26 63. The match lasted two hours and 23 minutes and Radwanska won just three more points than Rybarikova, 94 to 91; but at the end of the day Radwanska scored her 21st match win of the season, the second-most among anyone on the WTA - Sara Errani leads that stat with 22.
"She was very consistent and playing the same tennis from the beginning until the end," Radwanska said of Rybarikova. "It was also pretty tough conditions with the wind today, and she was using the wind very well from both sides of the court. She was serving very well too. When I broke in the third set I knew it was my chance to win the match, so I'm very happy I managed to do it in the end.
"I'm defending a lot of points here and I'm very happy to be through to the fourth round."