The tall Croatian's 6-2, 6-1 win over Sorana Cirstea, the third-seeded Romanian, was her career-best in ranking terms and was almost nervelessly taken despite the stressful conditions.
Vekic endured three hold-ups against the world number
24 in this Wimbledon warm-up event, all from exasperating rain delays, the last almost three hours long.
But her hard-hitting rhythm seemed largely unaffected.
"It was really difficult going out there so many times, but I tried to focus, and I think I was able to do that. It probably is my best performance so far," said Vekic.
The tall, blonde-haired teenager's appearance and her flat ground strokes were a little reminiscent of a famous 16-year-old who reached the semi-finals as qualifier in Birmingham exactly a decade ago.
That was Maria Sharapova, who consequently entered the top 100 for the first time and went on to become a tennis legend after winning this title and then Wimbledon the following year.
Vekic may or may not have mental qualities capable of matching those of the remarkable Russian, but she is ranked higher -- at 89 - than Sharapova was then, and seems comparably well-adjusted to grass.
"I think grass really suits my game. I like the speed of it and I like to dictate matches and I like to be in control in the points.
"Hopefully I can win Wimbledon. It's on grass, it's my favourite Slam and it's in London," added Vekic, who has spent half her time during the last four years living in London, and has a Londoner as a coach, David Felgate, former coach to Tim Henman.
Vekic's success was the second time in three matches that she had upset the seedings, having also won in straight sets against Urszula Radwanska, the eighth-seeded Pole .
She next has a meeting with a former champion, Magdalena Rybarikova, of Slovakia, who beat another highly promising player, Madison Keys, an 18-year-old American, by 6-3, 6-0.
Contesting the other quarter-finals were another former Birmingham champion, Sabine Lisicki, due to meet Alison Riske of the United States, three times a quarter-finalist, and Francesca Schiavone, the former
French Open champion from Italy, who was taking on Daniela Hantuchova, the former world number five from Slovakia.
Results from the fifth day of the WTA tournament in Birmingham (x denotes seed):
Donna Vekic (CRO) bt. Sorana Cirstea (ROU, x3) 6 – 2, 6 - 1
Magdalena Rybarikova (SVK, x16) bt. Madison Keys (USA) 6 – 3, 6 - 0