Australian Alpecin-Deceuninck rider Groves powered over the line ahead of Wout van Aert and Corbin Strong at the end of a 194 kilometre run between Cascais and Ourem in Portugal.
Visma's Van Aert takes the general classification lead after earning six bonus seconds for placing second.
"It's a really nice way to start this Vuelta," said Groves after his victory in five hours 12 minutes 55 seconds.
"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."
Van Aert now leads Brandon McNulty of UAE Team Emirates by three seconds overall, after the American took the red jersey after winning the stage one individual time trial.
Three-time winner Primoz Roglic, the Vuelta favourite, is 20 seconds off the top, while defending champion Sepp Kuss trails Van Aert by 56 seconds.
"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," said Van Aert.
"It was difficult to time the sprint well because the guys from behind maybe carried a bit more speed, so that's maybe something we should have looked (at), but Kaden passed me really strong and deserved his win."
Spaniards Ibon Ruiz and Luis Angel Mate made an early breakaway, the latter in his final season aged 40.
The peloton caught up with 52 kilometres to go and picked up the pace after a slow start.
The flat finale invited a bunch sprint finish and so it proved, with Groves delivering his fifth career Vuelta stage win.
Belgian Van Aert attacked with 200 metres to go but Groves powered beyond him to snatch victory.
Dylan van Baarle abandoned the race after a crash midway through the stage, a blow for his Visma team-mate Kuss's Vuelta defence hopes.
Monday's stage three remains in Portugal, taking riders 191.2km from Lousa to Castelo Branco.
