Primoz Roglic and Remco Evenepoel remain locked on the same time atop the overall standings with three stages remaining, including a summit finish on Friday.
Groves, who rides for the Alpecin team, pipped Frenchman Bryan Coquard at the line by using a late-thrust, bike-throw move to win by centimetres.
The race left the Pyrenean thermal spa village of Llivia at 1200m altitude for a 188km run to Sabadell.
A five-rider break never got too far ahead and Evenepoel's Soudal-Quick Step team made sure the race ended in a mass sprint.
Cofidis rider Guillaume Martin of France leads the King of the Mountains rankings on 40 points.
However, Friday's stage five from Tarragona winds back into the mountains for a run that culminates in a giant climb to a summit finish where stamina may start to sap.
