Van Aert (Visma-Lease a Bike) was held off by Groves (Alpecin-Deceuninck) in Sunday's stage but did take the overall lead and at the end of the 191.2km ride from Lousa to Castelo Branco he tasted victory in his Vuelta debut.
Spain's Jon Aberasturi Izaga (Euskaltel-Euskadi) finished third in the bunch sprint.
Van Aert increased his overall lead to 13 seconds over American Brandon McNulty thanks to the 10-second bonus for winning the stage.
"It's worth it to be patient. It's been quite a while since I could raise my hands and it feels so good," Van Aert said.
"I think I surprised him to go even before 200 metres. It was the perfect sprint for me."
The early part of the stage was dominated by a four-man breakaway group, which included Luis Angel Mate, the oldest rider in the race at 40, but it was his Euskaltel-Euskadi colleague Xabier Isasa who held out the longest.
He was finally reeled in with 20 kilometres left to ride, and the expected sprint finish was set up. With precious few sprint stages ahead in the Vuelta, Van Aert pulled out all the stops to ensure he was not denied for a second successive stage.
Tuesday's stage four brings the race to Spain after the opening period in Portugal, with a 170.5-km mountain stage from Plasencia to Pico Villuercas.
"Unfortunately the fun is over, tomorrow I'll be happy to give the role of team leader over to Sepp (Kuss) and Cian (Uijtdebroeks)," Van Aert said.
