"There is a lot of pressure when you know you have to win and your opponent has nothing to lose," Rublev commented.
Daniil Medvedev (2nd), Imperial since the start of the competition, will have the opportunity to qualify Russia for the last four if he beats the younger Ymer brothers, Mikael (94th at 23).
In the event of failure, the match would be decided between the pairs of Russian doubles Aslan Karatsev / Andrey Rublev and Swedish Andre Goransson / Robert Lindstedt.
Russia are aiming for their second Davis Cup semi-final in a row, after that won in 2019 by beating the Serbia of Novak Djokovic in the tie break (10/8) of the third set of the decisive double.
The Russians then lost to Canada.
Sweden has not reached the last four since 2007.
After an easily completed first set, Rublev gave up his opening face-off in the second set to be down 2-0.
The specter of his group match against Spain's Feliciano Lopez, lost after winning the first set 6-2, has loomed large.
Especially since, coming back and having served for the match at 5-4, he lost his serve twice in a row and let Ymer tie a set everywhere.
The two players remained neck and neck until the tie break where the Russian was able to make the difference in front of his mute captain Shamil Tarpischev who is celebrating his 100th Davis Cup meeting on the bench of Russia.
Tarpischev was first named captain of the Soviet Union in 1974. He is by far the most capped captain in the history of the competition.
The winner from Russia-Sweden will face Germany in the semi-final on Saturday.
The other semi-final will pit Novak Djokovic's Serbia against Croatia on Friday.
© 2021 AFP