• Paul, 25, ended Ben Shelton’s surprise run to reach a first major semi-final.
Nine-time champion Novak Djokovic reached the Australian Open semi-finals, sweeping aside fifth seed Andrey Rublev in a devastating display.
Serbia’s Djokovic, 35, cut a frustrated figure at times but channelled his emotions into a ruthless 6-1 6-2 6-4 win over Russia’s Rublev in Melbourne.
The fourth seed, who again had his left thigh strapped, will play American Tommy Paul in the last four on Friday.
Paul, 25, ended Ben Shelton’s surprise run to reach a first major semi-final.
World number 35 Paul won 7-6 (8-6) 6-3 5-7 6-4 against 20-year-old compatriot Shelton on Rod Laver Arena.
Former world number one Djokovic, who was the only major champion in the men’s quarter-finals, is favourite for the title as he chases a record-equalling 22nd Grand Slam.
Beating Rublev was his 26th consecutive win at Melbourne Park, equalling the Open-era streak recorded by American Andre Agassi.
Greek third seed Stefanos Tsitsipas will meet Russian Karen Khachanov in the other semi-final, also on Friday.
Paul, the first American men’s semi-finalist at the Australian Open since 2009, reached the fourth round of a major for the first time at Wimbledon last year and had not previously moved beyond round three at Melbourne Park.
But he further extended his best ever Slam run against big-serving world number 89 Shelton, who was bidding to become only the fourth man in the Open era to reach a semi-final within his first two Grand Slam appearances.
“Making it to the second weekend of a Slam is everyone’s dream when they start playing tennis, so I can’t believe I’m here right now,” said Paul.
Shelton, still taking online college classes, had never left the United States before travelling to Australia.
It has been a breakthrough tournament for left-hander Shelton, ranked outside of the top 500 a year ago, as he demonstrated his talent across four victories despite arriving in Melbourne with “no expectations”.
Shelton, who hit 24 aces, saw his opportunities limited as he fell two sets down against the consistent Paul, but he seized his chances in the third as he battled back impressively from a break down to force a fourth set.
However, Paul would not be denied again. He restored order with an immediate break of serve and went on to confidently serve out the biggest win of his career after Shelton, who left the court to a standing ovation, forced him to do so by saving a match point.