Putellas fired a rocket of a free kick into the top corner in the 11th minute, before Pina doubled the home side's advantage shortly after the half-hour mark with a well-placed finish.
10 minutes before the break Pina hit the crossbar, and Putellas was on hand to tap in the rebound as the home side completely outclassed the Swedes in the first half.
Although the visitors did better after the break, Pina struck her second late on to complete the 4-0 rout.
Earlier in the evening, Germany beat France 1-0 in Duesseldorf to take a slender lead into Tuesday's second leg, with the victorious semi-finalists set to contest the two-legged final on Nov 28 and Dec 2.
Sweden will require the most unlikely turnaround in Tuesday's second leg to reach the final.