The Belgian charged to victory at the end of the 191.2 kilometre run from Lousa to Castelo Branco in Portugal, having the power to stay ahead of Australian stage two winner Groves.
General classification leader Visma-Lease a bike rider Van Aert holds on to the red jersey, finishing in four hours 40 minutes and 42 seconds ahead of Groves and Spaniard Jon Aberasturi.
Van Aert secured his 10th Grand Tour stage victory having finished third and second on the opening two days of the Vuelta.
"It's worth it to be patient, it's been quite a while since I could raise my hands (in celebration) and this feels so good," said Van Aert after his first win since February.
"To use my strength and launch early... I think I surprised (Groves) by going even before 200 metres... it was the perfect sprint for me.
"The team was so strong, we had the whole race in control, they got me the perfect position in the end so this gave me the confidence to finish it off."
Van Aert will take a supporting role for his team-mate and last year's champion Sepp Kuss for stage four, the first chance for the general classification riders to take control.
"Unfortunately the fun is over, tomorrow I'll be happy to give the role as team leader to Sepp and Cian (Uijtdebroeks), it will be the first test for the GC guys and I will try to enjoy (wearing red) one more time," added Van Aert.
Kuss is one minute six seconds behind Van Aert, while three-time Vuelta champion and this year's favourite Primoz Roglic trails the Belgian by 30 seconds.
Spaniards Ibon Ruiz and Luis Angel Mate made an early breakaway for the second day running, with compatriots Unai Iribar and Xabier Isasa joining them.
The latter left the others behind but in baking Portuguese summer heat the peloton reeled in Isasa with around 20km remaining, with the stage profile inviting another bunch sprint finish, conquered by Van Aert.
The race enters Spain for stage four, running 170.5km from Plasencia to Pico Villuercas in the Extremadura region.
With a tough final climb in the Sierra de Villuercas mountain range the likes of Kuss and Red Bull–Bora–Hansgrohe's Slovenian veteran Roglic will likely dominate.
