Yates is set to complete an unprecedented clean sweep of this year's Grand Tours by British riders after Chris Froome's Giro d'Italia win and Geraint Thomas's victory at the Tour de France.
Spain's Enric Mas (Quick-Step Floors) and Colombia's Miguel Angel Lopez (Astana) finished first and second to put themselves on to the general classification podium with one stage remaining.
The victory will come as a relief for Yates, who led the Giro d'Italia in May for 13 stages before running out of gas as Froome clinched the title.
"Finally, I think it's sinking in," he said.
"I'm incredibly proud, and incredibly proud of the team also. They carried me through the entire three weeks. It's the first GT for the team - it's just unbelievable.
"In the last climb, I was really at my limit. Lopez and Mas they were really incredible in the final. I just tried to make my own rhythm. That was it, really. I gave it everything I had and thankfully it was enough."
Movistar's Alejandro Valverde entered the 97-kilometer stage in second place but he cracked on the final climb and lost more than three minutes.
The 38-year-old former winner slipped to fifth place in the overall standings.
Sunday's 21st stage is a flat 101-kilometer ride from Alcorcon to the Spanish capital.
(Reporting by Hardik Vyas in Bengaluru, editing by Pritha Sarkar)
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