Evans fought back from a set down to beat world No.49 Miomir Kecmanovic 3-6 6-4 6-4 to continue his strong run on the grass.
Victory in Eastbourne follows the 35-year-old’s statement win over top-20 player Frances Tiafoe at Queen’s last week, as Evans looks to rocket back up the rankings.
Evans, who has a career-high ranking of 21, was as low as 217 as recently as two weeks ago but his impressive showings on the grass leave him well-placed for a return to the top 150 ahead of Wimbledon next week.
“I am just happy to get another win,” he said. “I am not so interested on how it is; I am just trying to compete because I haven’t been playing much at this level in the last couple of years which has been difficult.
“Considering the conditions, I thought it was a very good level match. The last set was a little difficult because it was getting windier and windier. I knew before we went on that the forecast later in the day was more wind. I did well to come through and I played well when I needed to.”
Evans struggled to get a foothold in the first set, with Kecmanovic’s serve proving his main weapon but the Brit dramatically improved his own service game in the second to level the contest.
Heavy wind made life difficult for both players on the south coast, but Evans was able to come through for his second victory in a week over a top 50 player.
Evans, who has a main draw wild card for Wimbledon next week, faces second seed Tommy Paul in the next round, but the 35-year-old is not daunted by the prospect of facing the 2024 Queen’s champion.
“Tommy is a good player, I will have to play good tennis and compete hard to give myself chances and I am sure I will,” he added.
There also singles success for Fran Jones in the women’s draw, as she beat Greet Minnen 6-4 7-5.
Jones, who also has a Wimbledon wild card, is hovering outside the world’s top 100 but could be on course to break into single figures for the first time with a strong run at Eastbourne.
Victory over world No.70 Minnen was the perfect start and she will face either Magda Linette or Dayana Yastremska – both ranked in the top 50 – in the second round before a potential meeting with compatriot Sonay Kartal.
“The conditions were challenging here but that is for every player, so I don’t overthink it that much,” she said.
“I just try and use my virtues to the best of my ability. I am really content to get through it, it’s another match on the grass, another win at Tour level. I am just trying to keep my momentum.”
For the latest action on the British summer grass court season, check out the LTA website