On Wednesday evening, Rune won against Frances Tiafoe, who was forced to withdraw after Rune had won the first set 6-4 and was leading 3-1 in the second.
The American was clearly in pain, which helped tip the match in Rune's favour, so there was no doubt of the outcome in the second set.
In the quarter-finals of the Masters 1000 tournament, Rune will face the World No. 4, Taylor Fritz, if the American wins his match against the unseeded Terence Atmane from France later on Wednesday.
Rune's victory over Tiafoe ended up looking very convincing in the end, but the Dane was seriously challenged at the beginning of the match.
Already in his first service game, Rune was put under pressure, and he ended up giving away a break point, which the American took advantage of.
All in all, Rune struggled to settle in, and the Dane made an unusual number of unforced errors at the beginning of the match.
Rune was in danger of falling behind 0-4, but instead of losing the set, Rune recovered his stylish game and broke back soon after.
The 27-year-old American is known for his hard serve, but when Rune found out how to handle it, the Dane got the upper hand.
Rune broke to 5-4, and before the Dane could serve home the set a troubled Tiafoe received treatment and was given painkillers on the sidelines.
At the beginning of the second set, the world No. 14 looked uncomfortable, and the American looked resigned.
When Rune broke to make it 2-1, Tiafoe signaled that he wanted to give up, but his team convinced him to continue in the heat.
However, Tiafoe was no longer able to put up any significant resistance, and for fear of aggravating a potential injury, he had to withdraw.