Majka, who last year won the polka dot jersey for the mountains classification, powered away from the group of breakaway riders in the climb up the col du Tourmalet and never looked back.
The Tinkoff-Saxo rider beat Ireland's Dan Martin (Cannondale-Garmin) by one minute and German Emanuel Buchmann (Bora Argon) by 1:23.
Team Sky rider Froome finished ninth, 5:21 off the pace, having spent a quiet day in the group of leading riders, with none of his opponents trying to unsettle him.
He only lost two seconds to Spain's Alejandro Valverde, who sprinted in the finale to take eighth place.
A day after Froome and his Sky team mates hammered their rivals, there was a truce in the peloton.
"It was a hard day out there, a lot of guys, I, were feeling effects of yesterday's stage, but also we were keeping in mind we've got a very tough selective stage tomorrow," said Froome.
"The heat was a big factor."
Temperatures reached 35 Celsius in the Pyrenees on Wednesday, making for a particularly tough day after Tuesday's first mountain stage.
The stage win was contested by the eight men who formed the day's breakaway, after a fast start from Pau, as Team Sky allowed the group to build a decent lead.
Majka was the strongest and he attacked on the steep roads to the tourmalet -- a 17.1-km ascent at an average gradient of 7.3 percent -- to claim victory a day after his team leader Alberto Contador suffered a heavy defeat at La Pierre St Martin.
Froome still leads American Tejay van Garderen (BMC Racing) by 2:52 with Colombian Nairo Quintana (Movistar) in third place, 3:09 off the pace.
Contador is sixth 4:04 behind Froome and defending champion Vincenzo Nibali, who cracked in the final ascent of the day, a mild 6.4 km climb, dropped out of the top 10.
Thursday's 12th stage is another gruelling ride in the mountains, ending with the punishing ascent to the Plateau de Beille.
"We're expecting a big battle tomorrow," said Froome, who hinted he would ride defensively.
"For now I certainly don't need to be going and attacking. It just makes sense to follow the guys."
Froome, however, had said he would ride conservatively ahead of Tuesday's stage to La Pierre St Martin, before destroying his rivals to extend his overall lead.
(Reporting by Julien Pretot; Editing by Toby Davis)
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