The 18-year-old, who had never won a WTA main draw match on grass until this week, produced a fearless display on the slick grass court to beat the second seed and last year's Wimbledon runner-up 6-2, 3-6, 6-3.
Top seed and World No.2 Elena Rybakina also bowed out in London as she lost 7-5, 2-6, 6-4 to British wildcard Katie Boulter, fiance of Australia's No.1 Alex de Minaur, who was busy making his way into the semi-finals of the ATP grass-court tournament in 's-Hertogenbosch in Holland.
Both Rybakina and Boulter were playing their second matches of the day after rain washed out the entire programme on Thursday.
Former Wimbledon champion Rybakina had not hit a ball in anger all week after receiving a bye in the first round.
Earlier in the day she had come within two points of being sliced out of the tournament by defending champion Tatjana Maria, eventually finding her range to win 6-7 (7-4), 7-5, 6-0.
Rybakina also battled back from losing the first set against Boulter late in the evening and looked favourite to reach the semi-finals in the decider.
But Boulter then broke Rybakina's serve in the ninth game before serving out an impressive victory and setting up a semi-final against Croatia's lucky loser from qualifying Donna Vekic.
Vekic, ranked 76th, also had a busy day, first beating Czech Marie Bouzkova 7-6(9) 6-3 and then returning to beat another Czech, former No.1 Karolina Pliskova 6-4, 4-6, 6-3.
Jovic will face either Briton's Emma Raducanu, who beat Romania's seventh seed Sorana Cirstea 6-4 6-2, or Uzbekistan's Kamilla Rakhimova who outlasted British wildcard Harriet Dart.
