The 25-year-old Spain international was in lethal form in front of goal as a dominant Barca won the Clasico battle with ease at Camp Nou in front of over 40,000 fans, continuing their perfect start to the campaign.
The match was pushed back by two hours after torrential rain in the Catalonia region over the weekend.
Pina put Barcelona, who have won the league seven seasons running, in the driving seat after just four minutes with a neat finish after breezing into the area.
The Catalan side controlled the ball, and Madrid found it hard to pry it away from them, although they managed to fend them off until Pina's second in the 28th minute, the first of three goals in around five minutes.
Ewa Pajor's shot was blocked, and Pina polished off the rebound, completing her hat-trick a few minutes later by blasting into the top corner.
European champions Barca immediately struck again through Caroline Graham, who skipped past a defender before slotting home.
Pina bagged her fourth with a blast inside the near post before the interval as Barca yet again pulled apart Madrid's defence.
The fifth came early in the second half for Pere Romeu's side, through Polish striker Pajor.
Three-time Ballon d'Or winner Aitana Bonmati came on for the final 30 minutes as she continues her return to full fitness following a broken leg.
Swiss midfielder Sydney Schertenleib scored a stunning seventh from long range to round off Barca's rout late on.
Real Madrid have beaten Barca just once in 25 meetings between the sides across all competitions. Madrid's women's team began in 2020 after taking over CD Tacon.
