The longest stage of the race, a 200.5km ride from Villafranca Del Bierzo to Villablino, came down to a bunch sprint, and it was the Alpecin-Deceuninck rider who held off Van Aert who was looking for his fourth stage win.
New Zealand's Corbin Strong (Israel-Premier Tech) came in third, making it a repeat of stage two, when Groves had edged out Van Aert (Visma-Lease a Bike) for the win.
"I didn't actually expect today to be a sprint as it was but Visma controlled it and to have a man-on-man sprint against Wout is pretty awesome," Groves said.
"Today I didn't hesitate, I think I did a really good sprint. It felt like a drag race against Wout but it was great to beat him."
O'Connor (Decathlon-AG2R La Mondiale) retained the red leader's jersey, with a gap of one minute 21 seconds over Slovenia's Primoz Roglic (Red Bull-Bora-Hansgrohe).
Roglic had a mechanical issue in the closing stages, needing to take the bike of teammate Daniel Martinez, but he managed to make it back in time for the finish.
An early six-rider breakaway group was kept under control by the peloton, and they were reeled in on the final climb to set up the sprint finish.
Sunday's Stage 15 is a 143km ride from Infiesto to Valgrande-Pajares.
