Groves (Alpecin-Deceuninck) held off Van Aert (Visma-Lease a Bike) in a hectic finish to what had been a relatively sedate 194-km ride from the Portuguese coast at Cascais to Ourem.
Corbin Strong (Israel Premier Tech) came home third.
Van Aert was left frustrated at not winning a stage for the second successive day after Saturday's time trial but he took the red jersey by virtue of six bonus seconds.
"Of course, I wanted to win this stage, my team did a really good job to make it a bunch sprint so it's unfortunate to arrive second, but today I knew that finishing in the first three meant the red jersey, so after all it's a good day," Van Aert said.
Several riders were involved in a crash inside the last four kilometres with Ineos Grenadiers' Josh Tarling lucky to avoid serious injury as he crashed into a wall. All of them managed to reach the finish line and did not lose time.
The race became animated on the descent of a late climb with riders topping 80kph on the speed gun as they hurtled towards the finish. In the bunch sprint, Van Aert made the first move but Groves timed his effort superbly to take the win.
It was the Australian's fifth career stage win at the Vuelta.
"It's a really nice way to start this Vuelta. It's been a hard year for myself, not having a win yet, but I came here super motivated to change that, and I've got to thank my team for a really strong ride today," Groves said.
Monday's third stage stays in Portugal with the course taking the riders from Lousa to Castelo Branco.
