The 30-year-old caught and passed Colombian Santiago Buitrago with just 300 metres left of the mountainous 210km slog from Velez-Malaga to Penas Blancas.
"It's incredible, I really didn't expect this today," said Dunbar.
"I even said in the team radio after about 50 or 60km that today wasn't my day.
"I wasn't feeling good. Then I ended up in the break and my legs came around a bit."
Buitrago struck out for home inside the final two kilometres to distance his three breakaway companions, including Dunbar, who initially did not react.
But the Pinarello Q36.5 rider launched his counter attack in the final kilometre and wasted little time in reeling in Buitrago, who is the leader of the King of the Mountains competition.
Dunbar finished 14 seconds ahead of Buitrago, with his British team-mate, Thomas Gloag, coming home in third, 23 seconds back.
They had been part of an initial 16-man breakaway which only escaped around halfway through a chaotic stage, but then broke up on the final climb to the finish.
Mas comfortably held onto his 1min 37sec lead over four-time former champion Primoz Roglic as the overall contenders crossed the line together.
Roglic's Red Bull-Bora Hansgrohe team and the EF Education-Easypost outfit of former Giro d'Italia winner Richard Carapaz tried to increase the pace on the 18km final climb to the finish.
But they were unable to exert any pressure on Mas, who followed comfortably as he bids for a first Vuelta title after three previous second-place finishes.
