Off the front for almost the entire 171-kilometre test, the Polish national champion was active early and managed to push clear of the pack on the first climb out of Cistierna.
At just a little over five minutes off the red jersey Kwiatkowski and the six-man move represented a danger to the peloton, and as a result the group were marked closely by the bunch.
Despite not having much of an advantage to play with, Kwiatkowski still pushed clear on the Alto de la Falla de los Lobos, heading solo into the final kilometres before being swept up with just 3.5km to go.
That catch coincided with a number of attacks from the general classification contenders on the steep slopes of the Alto Les Praeres. David de la Cruz had been part of a group which gained some time on the run-in, but the Spaniard was eventually hauled back and set his own tempo on the first-category summit, finishing 25th on the day.
The result saw him slip to 16th overall, 6:57 back on returning race leader Simon Yates (Mitchelton-Scott). The Brit timed his late burst well to win the stage and take a 20-second race lead over Alejandro Valverde (Movistar).
Kwiatkowski’s gamble ultimately meant lost time at the line, with the Pole now 20th overall after a valiant effort, which saw him pick up the combativity award for the stage.
Team Sky began the day without Dylan van Baarle and were also forced to say goodbye to Pavel Sivakov after the Russian abandoned the race. “I was never able to recover from that nasty crash last Sunday. Today I couldn’t go any deeper,” he confirmed after showing plenty of promise during his Grand Tour debut.