In a largely nerveless performance, Evans grabbed his share of the limelight on a raucous Court 2, downing the Ukrainian 7-6(6) 6-4 6-1 by playing the key points better than his higher-ranked opponent.
In a country still licking its soccer wounds, the win revived the feelgood factor generated on Monday when self-confessed "loser" Marcus Willis dropped just 10 games in beating Lithuania's Ricardas Berankis, a player 718 places above him in the rankings.
"It's amazing what he's done," Evans told reporters.
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England's sporting image took a hefty battering in Monday's Euro 2016 defeat by Iceland, arguably the national team's most humiliating ever.
Evans believes tennis -- aside from Andy Murray's annual heroics traditionally a summer symbol of British under-achievement -- is capable of redressing the balance.
"I think this Wimbledon has opened the eyes of people that we're actually pretty good at tennis," he said.
"I think (the players) should be a bit more appreciated... Everyone puts the work in for the year (and) we're all trying as hard as each other."
With Willis, Evans and -- inevitably -- Murray all reaching round two or better and Britain holding the Davis Cup and, for the first time since 1978, boasting four men inside the top 100, the sentiment carries weight.
The lowest-ranked of that quartet at 91, Evans' progress to the third round of this year's tournament equals his best ever grand slam performance, matching his showing as a qualifier at the 2013 U.S. Open when he beat Japan's Kei Nishikori, now ranked world number six.
His plea for broader national recognition for his sport would become a roar if he wins his next match -- against seven-times champion Roger Federer -- who on Wednesday wrote the final chapter in Willis' Wimbledon fairytale.
"(Federer's) not a normal guy obviously, but he's another tennis player," said Evans, who like Willis has in the past faced accusations of failing to make the most of his talent.
"I just have to prepare myself and try and put that to the back of my head, that it's Roger I'm playing. Go out and give it my best."
(Editing by Martyn Herman)
