The fourth stage was a 184.6-kilometre ride from Andorra la Vella to Tarragona which included two category three climbs in the final 60 kilometres.
Coming into the final kilometre Groves was in an excellent position but had Juan Sebastian Molano (UAE Team Emirates) and Julius van den Berg (EF Education-Easypost) to contend with.
Van den Berg crashed into the barriers and it looked like Molano would take the stage when he went early. Coming off the final bend Molano held the lead but Groves powered home to take the stage win.
"Sebas (Molano) went full from the bottom with 350 metres to go and I was luckily patient enough and strong enough to close the gap with around 100 metres to go," Groves said after the race.
"I was confident I could pass him because he led out from very early. On a finish like that, which is super tough and long, I thought he would have to be on a really good day to beat me," the stage winner added.
Groves, who also won a stage at last year's Vuelta, was followed home by Molano in second and Edward Theuns (Lidl-Trek) in third place.
The stage had been billed as the first probable sprint finish of this year's race, but a three-man group who broke away at the start of the stage threatened to upset those predictions.
Eduardo Sepulveda (Lotto Dstny) was the first to be caught with just 22 kilometres left, but not after taking maximum points from both climbs to take over as leader in the mountains classification.
The other two riders in the breakaway, Ander Okamika (Burgos-BH) and David Gonzalez (Caja Rural-Seguros RGA) were caught by the peloton three kilometres later to set up the exciting stage finish.
There is no change at the top of the overall standings. Defending champion Remco Evenepoel (Soudal–Quick-Step) who won stage three still holds the red jersey and a five-second lead over Enric Mas (Movistar Team).
Lenny Martinez (Groupama-FDJ) holds onto third place ahead of this year's Tour de France winner Jonas Vingegaard of the Jumbo-Visma team.
Wednesday's stage five is a hilly 186.5-kilometre route from Morella to Burriana.
