Birrell, 27, the world No.77, bounced back from a first-round exit at Nottingham last week to put out Kenin, of the United States, 6-4 6-4 in the pre-Wimbledon tournament.
It provides more encouragement for Gold Coast resident Birrell, who has reached the quarter-finals in Singapore and Brisbane, along with ventures to the second round at Miami and Rosmalen so far this year.
She was also a success story at the Australian Open in January, where she won the mixed doubles with John-Patrick Smith.
Another Australian, Maya Joint, who eliminated two-time Wimbledon runner-up Ons Jabeur on Monday, has discovered that her reward will be a second-round clash with home favourite Emma Raducanu.
The British No.1 and seventh-seed had to recover from a first-set setback, deal with blustery conditions on England's south coast and manage a back problem on the way to a 6-7 (5-7) 6-3 6-1 win over Ann Li, of the United States.
She also revealed that she had received "some pretty bad news" but added: "so I would like to keep it personal, if that's OK?
"But it was difficult, very emotional at the end and probably just a release of different emotions."
Raducanu has been troubled by her back since competing in Strasbourg before the French Open and took an off-court medical timeout during her quarter-final loss at Queen's Club earlier this month.
But, aside from a slip and fall on the grass in set one, she appeared to come through her opening examination at Devonshire Park unscathed.
"It feels incredible. I want to thank the crowd for getting me through some really sticky moments," the former US Open champion said in her on-court interview.
"It really meant a lot to me and I'm really proud of how I fought back after losing the first set. I'm very, very happy to come through that.
"It was tough, it was up and down, but from the middle of the second set I think I found another gear and a another level."
Wimbledon champion Barbora Krejcikova retrieved two match points against British opponent Harriet Dart's serve before rallying to win her first-round tie.
Dart was 40-15 up on serve leading 5-4 in the decisive third set of a rain-affected round-of-32 match that second-seeded Krejcikova went on win 6-3 6-7 (4-7) 7-5.
It was just the second victory this year for the 17th-ranked Krejcikova, whose season did not start until May because of a back injury.
Jessica Pegula and Jasmine Paolini had contrasting victories on the Bad Homburg grass on as the two top seeds progressed to the last eight in Germany.
Top seed Pegula, of the United States, quickly dispatched qualifier Katerina Siniakova 6-3 6-2 in just over an hour.
But Paolini, Italy's No.2 seed, needed two hours and 32 minutes to beat Canadian Leylah Fernandez 7-6 (10-8), 7-6 (8-6) in the joint second-longest two-set WTA match of 2025 so far.
Poland's Iga Swiatek, the fourth seed who has never won Wimbledon despite five grand slam titles, also reached the last 16 after beating fellow former world No.1 Victoria Azarenka, of Belarus 6-4 6-4.
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