This group was caught out by splits, causing riders such as David de la Cruz (QuickStep Floors), Ilnur Zakarin (Katusha-Alpecin), Migel Angel Lopez (Astana) and Tejay Van Garderen (BMC Racing Team) to lose a small amount of time.
Froome countered Vincenzo Nibali's move on the final climb and widened his advantage over him by six seconds.
Nibali did gain four bonus seconds on Froome, but the Team Sky rider still heads the GC by 55 seconds from his Bahrain-Merida rival.
On the first of two key mountain stages this weekend, Majka - whose overall chances were undermined by illness in the first week of the race - was involved in an early break 20km in. We knew Majka was stronger than most of us in this kind of stage finish and his teammates did a great job in supporting him throughout. "The team has continued to believe in me and I am really excited".
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Froome is trying to win the Vuelta for the first time after finishing the grand tour runner-up on three occasions.
Briton Froome, who had bloody right knee and left elbow and hip pain from his crash in stage 12, found himself around the back of the red jersey group for large chunks of the stage, but withstood late attacks from Contador and Esteban Chaves to finish along with Nibali.
"Anything can happen", warned the Spanish (8th in 3 minutes and 19 seconds), at which it remains, "seven days of cycling in the legs" before retiring on the evening of the final stage, the 10 September in Madrid. The 15th stage is a 129.4-kilometer (80.4-mile) ride over two category-one climbs before a special-category finish at Alta Hoya de la Mora.