Spanish veteran Verdasco battled to a 3-6 6-4 7-6 (7-4) win over Kokkinakis in a match which included a heated exchange between the pair about the Australian qualifier's father at a change of ends in the third set.

Himself no stranger to controversy, Kyrgios also weighed in on the Kokkinakis-Verdasco exchange via Twitter.

During the almost three-hour showdown Kyrgios tweeted: "I hope TK wins this match, Verdasco is the saltiest dude, must be frustrated at his past success against Aussies."

The tweet was deleted after Kokkinakis, who won a deciding tiebreaker to knock Swiss world No.1 and defending champion Roger Federer out of the Masters 1000 event in the second round, was unable to get over the line against Verdasco.

The 34-year-old then responded to Kyrgios on Twitter: "@NickKyrgios when you have the courage to put a tweet insulting another player you need to have the same to don't delete it."

Kyrgios responded in kind.

"I honestly would have told it to Fernando's face, the reason I deleted my previous tweet was because I didn't want to cause unwanted attention, but I'm just gonna leave this here. Thanks for blocking me, I'm sure that took a lot of courage x," he tweeted.

Kokkinakis, who won a deciding tiebreaker to knock Swiss world No.1 and defending champion Roger Federer out of the Masters 1000 event in the second round, was unable to get over the line against 34-year-old Verdasco.

The flash point occurred when Kokkinakis took exception to the 31st seed disrupting him during his service motion and complained to the chair umpire.

Verdasco countered that a person behind him in the crowd, who he thought was Kokkinakis's coach, was constantly talking during his first and second serve. After a lengthy row, Verdasco said to Kokkinakis: "I'm not trying to disrespect you I'm not talking about you I'm talking about the guy in the crowd."

When Kokkinakis identified that it was his father who Verdasco was referring to, he replied: "That is affecting me. That's my f***ing dad."

Verdasco rallied from a 3-1 deficit in the third set and again from 3-0 down in the tiebreaker. After the match, the pair engaged in a frosty handshake.

It was a much smoother affair for Kyrgios, the 17th seed, who cruised to a routine 6-3 6-3 over 15th-seeded Italian Fabio Fognini, requiring just 66 minutes to progress.

"We both competed," Kyrgios told the ATP website. "I just played a little better in some bigger points."

Kyrgios was dominant on serve yet again and has not faced a break point in his two matches at Crandon Park.

"I knew it was going to be tough. He has a lot of tricks up his sleeve and he's very unpredictable," Kyrgios said. "I knew I just had to serve well, play aggressive and keep the points short."

Kyrgios, a two-time semi-finalist in Miami, has a 10-2 record at the tournament as he continues pursuing a maiden Masters 1000 title in just third event of an injury-hampered season.

He will meet fourth seed Alexander Zverev or veteran David Ferrer in the round of 16.

Spaniard and 16th seed Pablo Carreno Busta beat Steve Johnson 6-4 6-4 to set up a clash with countryman Verdasco.

Also reaching the fourth round were South African sixth seed Kevin Anderson, a 4-6 6-2 6-3 winner over Karen Khachanov, and 18-year-old Canadian Denis Shapovalov, who upset 11th-seeded American Sam Querrey 6-4 3-6 7-5.