Whybourn overcame Germany’s Sarah Gronert 6-1 4-6 6-4, a fine result for the world number 409 against a woman ranked nearly 250 places above her.
"I love playing here and feel really comfortable," Whybourn told the Wimbledon website.
"It’s a great opportunity for us being in our country that we get wild cards, especially the last month where we’ve all had some career best wins against people in the top 100.
"So we show we can compete at that level …and hopefully build on it."
Top-seeded Hungarian Melinda Czink and the fourth seed Misaki Doi of Japan also got through their opening matches, although second seed Eva Birnerova lost to Petra Rampre, who is actually ranked higher by the WTA.
There was less success for other British women on Tuesday, as Jade Windley, Katy Dunne, Anna Fiztpatrick, Tara Moore and Melanie South all lost their first-round qualifiers.
In the men's draw, 17-year-old Kyle Edmund's surprise run was halted by world number 276 Marcel Felder in the second round.
Having dispatched Daniel Gimeno-Traver of Spain late on Monday, Edmund met his match against Uruguay’s top men’s singles player Felder a day later, the Briton falling to a 0-6 7-6(2) 6-2 defeat.
"As the match wore on physically you get tired and mentally it’s quite draining,” Edmund said.
“If tight points, tight situations don’t go your way then you get a bit down but I had my chances.
"I think I was playing a bit too well in the first and he couldn’t get a rhythm. I think the first game when he held it’s like a brand new match, you can win in two sets which he did. He found his feet and started to play better.”
Joining Edmund on his way out of the competition was Chris Eaton, the only other Brit to reach the second round.
Eaton lost 7-6 7-6 to powerful Estonian and top seed Jurgen Zopp.
“It was really close and could have gone either way, it was a matter of a few points in the tie break and that was it so I am really happy that I managed to win those two tie breaks,” Zopp said.
“He plays completely different style than any other player here. He plays serve and volley and he doesn’t give you any rhythm. I think he played a great match.
"I didn’t play bad but he served unbelievably well. I don’t know how many aces he hit and a great first volley. It’s always tough to play these kinds of players.”
Meanwhile, Brian Baker secured a place in the third round with a no-nonsense 6-2 6-4 win over Germany’s Denis Gremelmayr.
Just one win now stands between Baker and a place in the main draw.
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