Contador attacked the Movistar rider on the descent from Port de Bales - the final climb of the day - to take victory in the queen stage by 13 seconds, and with it a likely overall victory.
The Tinkoff-Saxo rider engaged in a few mind games with Quintana on the ascent, but with the Tour de France just two weeks away, the Colombian says he wasn't willing to take any unnecessary risks.
"Contador made a strong attack halfway through the climb and I could respond pretty well," he said on the Movistar website. "At one point, he told me that should I take some turns [on the front], and that he'd let me win the stage.
"I told him that I wouldn't take any turns nor attack him. The roads into the descent were gritty, it made no sense to take any chances and lose everything; Contador made a really risky descent.
"I'm happy with how I rode today: my body responded well to the efforts."
Cycling Weekly looks at the Tour de France contenders
Thank you for reading 20 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1