1, who reach Sunday's Nottingham Open final, looked to have maintained that good form during a one-sided first set.
The Ukrainian led 30-0 on serve at 5-3 before the British No.1 won two games on the trot to tie up the set, and though Tsurenko saved two match points with courageous play in the tiebreak, a costly mid-point decision to challenge gave Konta the mini-break she needed to serve out the match. "It was so close to going to a third set".
Monday sees some of the finest players in men's tennis take to the court at Queen's for the Aegon Championship, while Birmingham hosts the women at the Aegon Classic. I think it was last year or the year before I think she made quarters or fourth round of Wimbledon.
Konta will be featuring in her sixth Wimbledon having never managed to get out of the second round so far.
"We are just staying very much in the process and also just keeping things in perspective - I am out here just trying to be the best player that I can be", she said. And I know she enjoys the grass.
Earlier, Petra Kvitova marked her return to her beloved grass with a 6-2 6-3 victory over fellow Czech Tereza Smitkova.
She said: "I think this first match on the grass was pretty good". "I'm happy that I have everything done with the media and the pressure and everything with the comeback in Paris. So I'm happy with that the most".
But Konta, who is playing in the Aegon Classic at Edgbaston this week, says that she will not be embracing any of the likely hype and intends to try to prepare as normal - inside her "bubble".
Fifth seed Kristina Mladenovic began her campaign with a 6-3 7-6 (7/2) victory over Duan Ying-Ying.
Nottingham champion Donna Vekic was not able to continue her winning run, losing 6-2 7-6 (7/2) to American Alison Riske.