Rune into Wimbledon quarters, 'not afraid' to face Alcaraz
World number six Rune came back from a set and a break down to defeat Grigor Dimitrov 3-6, 7-6 (8/6), 7-6 (7/4), 6-3.
He will tackle Alcaraz in the last eight if the top seed gets past former finalist Matteo Berrettini in his fourth-round clash.
"They are both great players, but I am not afraid. I am excited," said Rune, who was supported on Court One by Denmark's Crown Prince Frederik.
Rune, already a two-time quarter-finalist at the French Open, had been just two points from defeat in the previous round before seeing off Alejandro Davidovich Fokina in five sets.
On Monday, Dimitrov, the 24th-ranked Bulgarian who made the semi-finals in 2014, pocketed the first set after carving out a key break in the eighth game.
The veteran was a break ahead early in the second set, which 20-year-old Rune retrieved in the eighth game.
He levelled the match in the tiebreak.
After securing the third set, also on a tiebreak, Rune broke for 4-2 in the fourth courtesy of back-to-back double faults by Dimitrov.
Rune wrapped up the match, becoming the first Dane since Kurt Nielsen in 1958 to make the quarter-finals when Dimitrov pushed a weary backhand wide.
"Grigor is an amazing player, he pushed me to the limit," said Rune after a performance in which he fired 11 aces and 46 winners in total.
"It was a crazy match, tough and long. But I always fight to the end.
"I kept telling myself that Wimbledon is only once a year and that I have to fight to have any chance of winning."