Medvedev defeats Eubanks in five sets to reach Wimbledon semi-finals
The world number three from Russia triumphed 6-4, 1-6, 4-6, 7-6 (7/4), 6-1 and will face either top-ranked Carlos Alcaraz or sixth seed Holger Rune for a place in Sunday's final.
Former US Open champion Medvedev hit 52 winners compared to Eubanks' 74 but crucially committed just a meagre 13 unforced errors to his opponent's 55.
Eubanks, who had shocked fifth-ranked Stefanos Tsistipas in the previous round, was attempting to become just the third man to reach the semi-finals on debut.
However, the 27-year-old's challenge fizzled out in the final set of a bruising, big-hitting contest.
"After the first set, I didn't want to go five sets but when I lost the third, I was happy to go five," said Medvedev who fired 28 aces.
"There were moments in the match when I was losing the game so to say and he was playing well.
"I started to sink and make mistakes but after the third set I started to build something. I had more opportunities in the fourth set and after the tiebreak I played amazing."
Medvedev was untroubled in the opening set, carving out the only break in the third game before claiming the opener in which he committed just one unforced error to 11 for Eubanks.
However, the American soon found his range with his one-handed backhand, pocketing a double break in the second set before levelling the quarter-final with his seventh ace.
The world number 43 had his tail up and a break in the opening game of the third set was the platform as he moved towards a two sets to one lead.
A frustrated Medvedev was handed a code violation for lobbing a ball that hit a courtside camera operator in the eighth game.
An unreturned serve gave Eubanks the set.
Serve dominated the fourth set as Eubanks passed 100 aces for the tournament but it was the more composed Medvedev who claimed the tiebreaker when the American buried a backhand volley into the net.
Suddenly the spirit seeped out of Eubanks' all-out attacking game as he slipped to a key double break down in the decider.