Cobo completed the final stage with his 13-second advantage, the seventh smallest margin in a Grand Tour for more than five decades, intact.
However, on Sunday's 95.5 kilometre run to Madrid the Geox rider did not drink any champagne as he rode along or do any other on-bike celebrations, as is traditional for the overall winner on the largely ceremonial last stage of major Tours.
"Finally there were no attacks but I was worried," Cobo said after completing the stage in 20th place and receiving the winner's trophy from Prince Felipe, heir to the Spanish throne.
"I'd like to thank (Froome's team) Sky publicly for not trying anything at the last minute.
"I relaxed a little when I saw they weren't try to pull back the breaks, and in fact I still can't believe I've won now."
Froome told Reuters he would not have attacked Cobo on the final stage.
"It would have felt a bit like cheating," he said.
"I had my chance in the mountains. You don't attack the leader on the Champs Elysees stage in the Tour de France, and the same goes for here in the last stage of the Tour of Spain."
Froome's Sky team-mate Bradley Wiggins, also of Britain, finished third overall, his best ever result in a major Tour after taking fourth in the 2009 Tour de France.
"It's a big step forward," Wiggins told Reuters.
Nicknamed 'the Bison', Cobo galloped into contention with a late attack on the Farrapona climb on stage 14 that enabled him to climb to eighth overall.
Then the 30-year-old Geox rider struck hard again on the decisive Angliru summit finish on stage 15 to oust Wiggins from the lead.
Froome hit back in the short but very steep Pena Cabarga climb to close the gap to 13 seconds and win his first ever Grand Tour stage.
But Cobo responded to the Kenyan-born rider's attack on the two final mountainous stages in the Basque Country to claim a victory by the third narrowest margin ever in the Vuelta.
Whilst Cobo's previous best placing in a major Tour was 10th in the 2009 Vuelta, Wiggins and Froome are the first top-three finishers for Britain in a Grand Tour since Robert Millar in the 1987 Giro d'Italia.
The final stage win went to Peter Sagan of Slovakia, ahead of Italians Daniele Bennati and Alessandro Petacchi in a bunch sprint.
Victory in the points competition went in a last-day switch to Dutchman Bauke Mollema, with France's David Moncoutie winning the Vuelta's King of the Mountains competition for the fourth year running.