Yates will take his advantage of 1 minute, 46 seconds, over Enric Mas into the final stage, when race custom dictates the riders don't attack the race leaders on the traditional arrival to Madrid.
"I've made it! It's still sinking in," said Yates, who rides for Mitchelton-Scott.
"I'm incredibly proud. I'm also incredibly proud of the team. They've carried me for these entire three weeks. It's the first Grand Tour for the team. It's just unbelievable."
Mas moved into second place overall with the stage victory. The Spaniard edged Miguel Angel Lopez of Colombia at the finish of the short but incredibly demanding 97-kilometer (60-mile) route in the tiny nation of Andorra tucked in the Pyrenees Mountains. Riders faced a constant up-and-down route over six categorized climbs including a finish atop the beyond-category Coll de la Gallina.
Andorra is where Yates and his twin brother Adam Yates are based. Adam helpd Simon withstand the fast pace set by Lopez's Astana team midway through the stage, then Simon attacked on the fifth climb to ensure he kept the red jersey.
Alejandro Valverde entered the stage in second place, but he withered under Yates' attack and the pursuit by the other top riders. The 38-year-old veteran fell to fifth place in the overall standings.
"It felt like it would never end," Valverde said. "I was completely spent by the end and could only focus on finishing."
Yates was third to cross the finish line, around 20 seconds behind Mas and Lopez, who completed the brutal test in just under three hours.
"Sometimes attack is the best defense. In the last climb I was OK. I was at my limit," Yates said. "Mas and Lopez were riding incredible. I just tried to make my own rhythm. I gave everything I had and thankfully it was enough."
Yates led the three-week race on Stages 9-11, and then won Stage 14 in the northwestern Picos de Europa mountains to reclaim the red jersey for good.
The biggest win of Yates' career compensates for his near miss in the Giro d'Italia in May. He led the Giro for 13 stages before ceding the lead with two days left to eventual winner Chris Froome.
Yates' win of the Vuelta will also complete a sweep by British riders of the season's three Grand Tours. Geraint Thomas won the Tour de France in July.
Yates first made his mark on the track, winning the Madison at the junior worlds in 2010. Three years later at the senior worlds, he won the points race. He made his Grand Tour in the 2014 Tour de France. On last year's Tour, he emulated his brother's achievement in winning the young rider's classification, finishing seventh overall.
Mas has been the revelation of this Vuelta. The Quick-Step rider, who had only one career stage win at the Tour of the Basque Country in April, impressed with his strong form in the mountains.
"I'm a young 23-year-old kid enjoying myself," Mas said. "I've been dreaming of this for years."
Lopez moved into third place in the general classification.
Valverde's Movistar teammate and fellow former winner, Nairo Quintana, fell to eighth place.
Sunday's 21st stage is a flat 101-kilometer ride from Alcorcon to the center of the Spanish capital.
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