It was difficult to tell which club was challenging for a top-three spot and which one was battling to avoid a relegation battle as Cagliari tormented Fiorentina goalkeeper Neto for over an hour in Sardinia.
Pinilla scored a penalty shortly before half-time to lift Cagliari into 13th place while Vincenzo Montella's Fiorentina could now see Inter Milan close to within five points of taking fourth place with victory at Juventus on Sunday.
It would not be a comfortable night in the Fiorentina goal for Neto, who found himself scrambling to smother the ball at Pinilla's feet in the early stages following a fine through-ball from Marco Sau.
Cagliari enjoyed a better chance when Stefan Savic lost the ball in a dangerous area. Neto stopped Pinilla from clipping home an easy tap-in and then watched gratefully as Daniele Dessena smashed the rebound wide.
His luck ran out in the 39th minute as Facundo Roncaglia brought Sau down in his area, with Pinilla requiring little encouragement to drive his spot-kick straight down the middle of the goal.
Neto was praying to hear the half-time whistle when Daniele Conti's free-kick took a killer deflection off the wall to end up with Sau, who lost control of the ball before he could pick his spot from close range.
When play resumed Neto was panicking once more as Savic lost possession to Sau on the edge of the area.
But as the Viola goalkeeper steeled himself for the one-on-one, Savic tracked back to make amends for his mistake by recovering the ball.
Fiorentina finally broke forward after the hour mark and Davide Astori needed to cover for Cagliari keeper Vlada Avramov as Alberto Aquilani - who scored a hat-trick against Genoa last time out - loped into the hosts' box.
David Pizarro and Alessandro Matri warmed Avramov's palms as the Tuscans grew into the game late on but still Cagliari dominated the attacking plays, Pinilla twisting on the spot to test Neto with a low shot to the near post.
Even though Fiorentina's race had been run for some time, they were relieved to see the flailing Savic manage to avoid scoring a calamitous own-goal from Conti's cross deep into stoppage time.