It was a third straight win behind closed doors at the controversial stadium, from which Rossoblu fans are barred due to ongoing safety concerns, and on Saturday's evidence they may choose not to apply for re-entry for the four remaining home games.
Pinilla needed 11 minutes to beat Emiliano Viviano before firing the winner from the penalty spot just before half-time.
Juan Cuadrado's second-half response gave Fiorentina brief hope they could make up ground on third-placed AC Milan, but they remain fourth while Cagliari climb to 11th.
It was clear today would belong to Cagliari from the early exchanges as Marco Sau came dangerously close to tucking home Pinilla's deflected header.
They would not wait long as the Chilean found the net with a deft shot beyond Viviano having been played onside by Facundo Roncaglia.
Fiorentina were, uncharacteristically, struggling to take control in midfield and Stevan Jovetic was restricted to an acrobatic effort from an uncomfortable angle in the 20th minute.
The Montenegrin's afternoon ended prematurely on the half-hour mark as injury forced Marcelo Larrondo into an early appearance from the bench.
The loss of their talismanic striker further unsettled La Viola and Cagliari took advantage of the malaise to double their lead six minutes before the break.
When Cuadrado was adjudged to have impeded Sau in the area, Pinilla stepped up to beat Viviano from the spot to a ripple of applause from the home dugout.
Adem Ljajic might have settled his side's nerves with an away goal before the break but his first touch was lacking and his shot sailed wide of the mark.
Fiorentina continued to struggle without their fans roaring them on when play resumed and Manuel Pasqual inexplicably opted to pass to Larrondo with the goal at his mercy.
The only way in was from distance with Cagliari closing ranks and in the 74th minute Cuadrado found the gap he needed to spin Nicola Murru and drive the ball home on the turn.
That move transferred the jitters to the Sardinians for a frantic closing period and Alberto Aquilani was first to threaten the equaliser, instead spooning over the bar when he needed a more delicate touch.
Then, two minutes into stoppage time, substitute Luca Toni bamboozled Michael Agazzi with a shot on his less-favoured left foot, but the ball trickled agonisingly wide.