World number 62 Evans, who has won just one match in seven French Open main-draw appearances, was unable to equal his best run in Paris as two-time quarter-finalist Rune claimed an impressive victory.
Evans, the British number three, dug in to save two break points in a gruelling 13-minute third game on Court Suzanne Lenglen, but Rune eventually made his breakthrough for a 5-4 lead before serving out the opening set.
Evans came through another thorough examination at the start of the second set, saving four break points, and launched a positive response by creating his first opportunity on Rune’s serve.
However, it was again Rune who struck first – and the single break again proved enough after he produced a second-serve ace to save a break point when serving for a two-set lead.
The Briton was frustrated after Rune immediately broke back midway through a must-win third set, and the pair exchanged words after Rune disrupted Evans’ service game to dispute a line call with the umpire.
Evans, who was fined after a recent argument with an umpire in Rome, said afterwards: “I’m fed up with the umpires, full stop.
“I feel like I’m on a roll and and I was disrupted, but it’s not Rune’s fault if he’s allowed to have a conversation.
“It was just a chat – and I’m waiting to serve. It’s freezing on the court, the match was flowing great and then it just stopped in the middle and I don’t understand.”
Having levelled the set from 4-2 down, Rune maintained his momentum to make the decisive break before completing victory on serve by taking a fourth successive game.
“That’s not the reason I lost,” added Evans. “That’s just part of the issue, part of the problem, but he [the umpire] will be back in work again tomorrow.”
Evans, who lost in the first round at the Australian Open in January, will return to action alongside Murray in the men’s doubles – the start of which was delayed by persistent rain on Tuesday.
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