The Frenchman, 33, paid a faulty service, weighed down by eight double faults, and too many unforced errors in total (21 against 10), which allowed his opponent to break him three times in five opportunities.
On the other hand, Paire could not convert the four balls he obtained to steal the commitment of his rival and try to return in a game finally concluded in 1h18 by Rune, on his fifth match point.
The latter will face the Canadian Denis Shapovalov or the American Jeffrey John Wolf, opposed during the day.
Leaving the world top 100 at the start of the week after a series of six defeats in the first round, Paire broke this bad series on Monday at the expense of the German Peter Gojowczyk (7-5, 6-4).
However, the Avignonnais, who was still 20th in the world at the start of 2020 before the coronavirus pandemic, did not exceed the round of 16 of a tournament in 2022.
© 2022 AFP