The Serbian second seed's match against France's Adrian Mannarino was delayed because of the epic five-setter between Gilles Muller and Rafa Nadal.
From then on, it is women's quarters all the way.
Five-times champion Venus Williams is, at 37, the oldest player in more than two decades to reach the last eight. The American faces 20-year-old French Open champion Ostapenko from Latvia.
Next up is second seed Halep, who will become the first Romanian woman to reach world number one if she beats Konta. The British sixth seed is looking to become the first home women's champion for 40 years.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
On Court One, Russia's Svetlana Kuznetsova - in the Wimbledon quarter-finals for the first time in 10 years - will go up against Spain's Garbine Muguruza, who eliminated world number one Angelique Kerber on Monday.
Wrapping up the women's quarter-finals, big-hitting Coco Vandeweghe from the United States will hope her new coach Pat Cash, a former Wimbledon champion, will give her the edge as she takes on Slovakia's Magdalena Rybarikova.
(Reporting by Pravin Char; Editing by Peter Rutherford)
