Tarling, 19, died in a crash with a vehicle at a race in Portugal earlier this month. His brother, Josh, rode alongside Pidcock for Netcompany Ineos in 2023.
"I don't have much words to be honest, it was a hard road here after the Tour," said an emotional Pidcock, who finished ninth at July's Tour de France.
"I want to dedicate this win to Fin Tarling, to Josh. Seeing him start the Vuelta was pretty incredible, so I dedicate it to him and his family."
Josh Tarling had started the Vuelta a Espana Grand Tour just days after his brother's death and came close to winning the opening stage time trial, although he quit the race just a few days later.
On Sunday in Val di Sole, Briton Pidcock started on the fifth row and was forced to overtake numerous rivals before finally hitting out alone at the front on the seventh of eight laps.
Fellow Briton Charlie Aldridge finished second with Canada's Cole Punchard third, while star Dutchman Mathieu van der Poel, a world champion on the road and in cyclocross, was never able to make his mark and came home in 30th.
Pidcock, 27, is a two-time Olympic mountain bike champion from Tokyo, in 2021, and Paris 2024.
The Leeds native also won a Tour stage on the iconic Alpe de Huez climb in road cycling and won the cyclocross world title, both in 2022.