Berdych, a two-time semi-finalist, was too cool and focused for the easily distracted 20-year-old, winning 6-3, 6-4, 1-6, 6-4 in a rowdy night match on Rod Laver Arena.
The Czech sixth seed advanced to the last 16 for the sixth consecutive Grand Slam where he will face Spaniard Roberto Bautista Agut, who knocked out 2014 US Open champion Marin Cilic in straight sets.
The big-serving Berdych, faced with a partisan home crowd, mastered the occasion breaking Kyrgios’s serve three times, while the madcap Aussie repeatedly clashed with the umpire and engaged in a long-running conversation with himself.
Kyrgios sad that he lost, feels he let ppl down. Told by a journalist that everybody loses, he responds: "Djokovic doesnt lose"— Reem Abulleil (@ReemAbulleil) January 22, 2016
The Czech iron man, who upset Rafael Nadal on the way to last year’s semi-finals, won the majority of the longer rallies and hit 44 winners, 26 of them on his big forehand.
Kyrgios gave his home supporters some hope with a fightback in the third set when he twice broke Berdych’s serve, but the Czech regrouped in the fourth set to clinically finish off the Aussie.
Kyrgios was defending ranking points after making the quarter-finals in last year’s event, where he lost to Andy Murray.
The six-time Melbourne Park winner and defending champion easily out-muscled the overawed Russian on Rod Laver Arena in just 44 minutes, the shortest match of the tournament so far.
It sets her up with a fourth-round clash against another Russian, Margarita Gasparyan, with a quarter-final beckoning against old foe Maria Sharapova — a showdown Williams would be confident of winning.
She has beaten Sharapova in every match they have played since 2004.
“I think I played well today. It was one of those days where everything I did went right,” said the 34-year-old, who offered some word of encouragement to Kasatkina.
“She has such a bright future. She’s so young and she’s headed in the right direction.”
Playing on centre court against the top seed at a Grand Slam was a huge occasion for the 18-year-old, who was not only making her debut at the tournament but is on her first ever trip to Australia.
The teen only played her first WTA tournament last April, but has so far managed to score three wins over top 50 opposition, signalling her promise.
She came into the event as the world’s 69th-ranked player but was no match for the composed and massively experienced American, who is gunning to equal Steffi Graf’s Open-era record of 22 Grand Slam titles.
The powerful Williams wasted little time in laying down the law, winning a break for a 2-0 lead with Kasatkina barely getting her racquet on the ball as she was pushed around the court.
Kasatkina managed to get on the scoreboard in holding serve for 1-3 but she had no answers to Williams’ serve as the American rattled through the set in just 22 minutes.
After her second-round win, Williams said she was pleased by her consistency and lack of errors, and it was a similar story on Friday.
The American, who dropped only three matches in 56 last season, made few mistakes in a dominant display and broke in the first game of the second set with outgunned Kasatkina struggling against the Williams weaponry.
She didn’t give up and won a service game to be 1-2, but that was as good as it got as Williams cantered to the finish line.
Williams won three majors — the Australian and French Opens and Wimbledon — last year which took her to within one of Graf’s long-time record of 22.
She claimed her first Australian Open title in 2003, beating sister Venus in the final, and reached her sixth last year when she toppled Sharapova.
The 10-time Grand Slam champion survived two set points in a final set tiebreaker before completing a 6-1, 7-5, 7-6 (8/6) win and his 12th straight over Seppi, and will now play Frenchman Gilles Simon.
Djokovic has now reached the round of 16 at the Australian Open for a 10th straight year. The world’s top player also holds a 33-match winning sequence against Italian opposition.
Djokovic was facing two set points in a third-set tiebreaker before he reeled off four straight points to take the match in two hours, 21 minutes. He is yet to drop a set in three rounds at the year-opening Grand Slam.
“I started the match very well with great intensity and I played some very solid tennis for the first 30-40 minutes,” Djokovic said.
“He then stepped it up, he started serving well and he has a very quick game from the back of the court with a lot of depth so I backed up and did a lot of defending.
Djokovic delivers... The defending champ makes the R16 for 10th straight year, downing Seppi 6-1 7-5 7-6(6). pic.twitter.com/ZWYzVtB95a— Australian Open (@AustralianOpen) January 22, 2016
“It was very close in the last two sets and could have gone either way.”
Djokovic whistled through the opening set, with two service breaks in just 25 minutes, but he encountered stiffer opposition in the following set.
The Serb top seed had a break point on his serve in the seventh before breaking the Italian in the 11th game.
Djokovic served out for a two sets lead over Seppi, who has taken just one set off Djokovic in eight hardcourt encounters.
Seppi ambushed Roger Federer at the same stage at last year’s Australian Open, but the top seed was always in command on Magaret Court Arena.
Even when he was two set points down, he still found a way to reel off the final four points to take the match and advance to the last 16.