Froome, who is bidding to become only the third rider to win La Vuelta and the Tour de France in the same year, crossed the line 31 seconds down on the Polish rider after the 175km stage.
"Once I was there I said "today can be again my day".
"I was aware of the bonus seconds at the end but I wasn't too bothered to be honest", said Froome. "They trusted in me and did a great job".
"I had confidence in rolling to a tempo stable because I knew that the climb was long".
"It was hard to keep up with the pace because we were going very fast ahead and in the middle part, it would have been quite comfortable in the main group behind", he added. "It was like a time trial from there".
He said: 'It's an incredible feeling to finish off today and still to be the leader of three competitions - the red, the white and the green jersey as well - and to have survived a stage like today.
At the time of going to press, Chris Froome is still leading the pack after he finished second on the 11 stage, 187.5km route from Lorca to Observatorio de Calar Alto.
The state has tried without success to décramponner Chris Froome (Sky) on the final climb: supported by the Spanish Alberto Contador (Trek), Nibali accelerated on several occasions, but the British returned to the train.
A late surge by Froome over the final meters of the punishing ride and a final special-category ascent allowed him to increase the gap over Vincenzo Nibali from 55 seconds to 1:01.
The Italian took his third win of the Vuelta so far, tightening his claws into a Green Jersey that now looks very likely to be his when the field comes into Spain on the 10th September.
Majka ensured he was part of the 10-man breakaway that formed a spearhead roughly midway though the stage, but that bunch had been whittled down to just six or so at the penultimate climb, a category-two mountain about 30 kilometres from the finish.