Madrid took a surprise lead against their all-conquering rivals when Olga Carmona fired in early at the Alfredo di Stefano Stadium and the home side had chances to extend their advantage, with Esther Gonzalez hitting the post.
Instead, Barca came storming back, aided by a soft penalty, which was converted by Ballon d'Or winner Putellas, before Claudia Pina and then Putellas' second completed a devastating turnaround.
It will take a monumental effort from Madrid to prevent the Catalans reaching the semis, particularly as the second leg will be played at Camp Nou, in front of what is set to be a world-record crowd.
Real Madrid said they were unable to use the Santiago Bernabeu for this first leg due to ongoing renovation work at the club's main ground.
Barcelona came into the women's Clasico as hot favourites after winning all five of the competitive meetings with Real Madrid since Madrid officially launched their women's team in 2020.
While Madrid sit fifth in the Primera Division this season, Barca are 19 points clear at the top of the table, having registered 24 wins out of 24, scoring an astonishing 136 goals in the process.
They retained the title earlier this month with six games to spare, by thrashing Real Madrid 5-0.
But Madrid were far from over-awed, their performance offering hope they can continue to close the gap next season, even if their chances of progress look remote.
Putellas missed an early chance at the back post from Mapi Leon's cross and then it was Putellas who was at fault for the opener, her sloppy pass allowing Real Madrid to break.
Esther weaved through and as Barca's defence were drawn inside, she shifted the ball left for Olga, who guided a cool finish into the corner.
Esther struck the post after chesting down Claudia Zornoza's lofted ball over the top and hooking a shot towards goal and then Esther went through again, this time shooting straight at Sandra Panos.
But Barcelona improved in the second half, rejuvenated by their equaliser in the 53rd minute.
Fridolina Rolfoe's cross reached the back post and as the ball bounced, Olga arrived late, her knee making contact with Barca's Caroline Graham Hansen, who made the most of the fall.
Finnish referee Lina Lehtovaara was initially unconvinced but, after consulting the replay, gave the penalty. Misa confronted Putellas on the spot but the attempted mind-games had no effect, Putellas finding the corner.
With the score level, Barcelona were suddenly sharper and more assertive and by the final 10 minutes a weary Madrid were hanging on.
Barca would not be denied as Pina surged forward and played right for Hansen, whose cut-back found Aitana Bonmati in the area. Bonmati's finish was blocked but the ball spilled fell kindly for Pina, who drove low and into the corner.
Madrid had lost the match and in injury-time they likely lost the tie, as Barcelona broke down the right and Putellas was left free in the area. She scooped a delightful finish into the net.