With world No. 1 Novak Djokovic also cruising through the third round beating flamboyant Czech Radek Stepanek 6-4, 6-3, 7-5 on Rod Laver Arena, at Hisense Anderson beat Verdasco in five sets, 4-6, 6-3, 4-6, 7-6 (4), 6-2 to knock the popular Spaniard out of the Australian Open.
On Margaret Court Arena, Serbia's Tipsarevic beat Frenchman Julien Benneteau 3-6, 6-4, 2-6, 6-4, 6-3, Japan's Nishikori downed Russia's Evgeny Donskoy in three sets, 7-6 (3), 6-2, 6-3 and Spain's Almagro also cruised past Polish big man Jerzy Janowicz 7-6 (3), 7-6 (4), 6-1.
Anderson caused the big upset of the day, though, knocking out 22nd seed and former world No. 7 Verdasco in five sets. Verdasco took the first 6-3, but the big-serving Anderson dominated the second to level things when he took it 6-3.
The Spaniard left-hander hit back to win the third 6-4 and appear to be in control after easily breaking Anderson's serve, but the 26-year-old South African had already beaten Verdasco once this Australian summer at the Hopman Cup and had the confidence to do it again.
He controlled the fourth set tie-break after missing a chance to serve out the set, and broke down Verdasco in the fifth winning it 6-2 to advance to the fourth round of a Grand Slam for the first time in his career.
It was a disappointing exit for Verdasco, who made the 2009 Australian Open semi-final, and copped a code violation along the way for letting off steam verbally, but it's a big result for Anderson who now will face the winner of the Jurgen Melzer-Tomas Berdych third round match.
Anderson was delighted to prevail over the Spaniard after just under four hours out on court.
"It was a great match and it was realy close," Anderson said.
"I knew it was a very important match for me. I have played Fernando twice before, but they were both on clay courts and he beat me both times. Even though it wasn’t the same format, it was great to get that win over him at the Hopman Cup and that gave me a lot of confidence coming into today.
"After serving for the fourth set, all of a sudden we were in the tie-break and I was obviously very happy to get through that and I thought I picked it up nicely in the fifth set there."
It was another five-setter on Margaret Court Arena, but eighth-seed Tipsarevic had to fight back from a big hole to advance.
Frenchman Benneteau was in control leading two sets to one with the Serbian looking to have run out of legs after tough matches with Lleyton Hewitt and Lukas Lacko in the first two rounds.
However, nobody told Tipsarevic that and he fought his way all the way back to win the last two sets 6-4, 6-3 to advance to the fourth round where a clash with Spaniard Almagro awaits.
Tipsarevic was relieved after the match to have got through after being down two sets to one.
"I think it's good for the crowd to watch me play matches like this, but it's not good for my legs. Right now I feel really, really tired but can only can consider myself lucky to win a match like this," Tipsarevic said.
"On a windy day like this I really feel like it could have gone either way. Julien played a good match and nobody know until the end who was going to win. I really consider myself lucky being the winner on today's match."
Almagro booked in his fourth round clash with Tipsarevic by cruising past Polish big-hitter Janowicz.
The Pole 24th seed was always likely to cause Almagro some problems with his height and power game, but after two tie-break sets that the 10th seed Spaniard won, he cruised through the third set 6-1 to wrap up the victory.
The other men's third round clash to be completed so far on Friday saw Japan's Nishikori comfortably account for Russian Donskoy in three sets. Nishikori will now face the winner of the David Ferrer-Marcos Baghdatis third round clash.
If he wins that fourth round match it will equal his performance last year in Melbourne where he lost in the quarter finals to Andy Murray after beating Jo-Wilfried Tsonga.