Pulga is an icon in Sardinia as a result of his playing days, and has done little to change that since taking the managerial reins from Massimo Ficcadenti last month, winning all four of his games in charge.
But La Viola put a stop to that in resounding fashion on Sunday, with goals from Gonzalo, Stevan Jovetic, Luca Toni and Juan Cuadrado putting them into fourth place. Federico Casarini had equalised for Cagliari who left the Stadio Artemio Franchi with their bubble well and truly burst.
They had not looked set for such an outcome early in the game, with Andrea Cossu going close for them with a six-yard drive which flashed just over.
But their failure to cash in on their early-stage dominance would cost them as Fiorentina took a 14th-minute lead, with Gonzalo's header scraping under the bar after a precise cross from Borja Valero.
Trailing is not a position the Rossoblu have become accustomed to under Pulga, and they did their best to try and get level, with Thiago Ribeiro firing over from distance and Cossu drawing a save out of Emiliano Viviano.
There was a crispness about Fiorentina's play, though, and David Pizarro nearly finished off a flowing move as the break approached before, with three minutes of the half left, Cagliari got the goal they craved, with Cossu's free-kick finding Casarini who did the rest.
It was perhaps harsh on the hosts to have been level at the break, for they had been the better team, but five minutes after it, they were back ahead, with Jovetic volleying a loose ball beyond Michael Agazzi.
Cagliari came back well and Marco Sau's effort was scrambled off the line - a moment that would prove decisive as Toni gratefully took in Valero's brilliant pass and put his side two clear a minute later.
The former Italy striker had broken Cagliari's spirit and from then on it was a matter of how many more Fiorentina would score, with Pizarro again trying, before Cuadrado got the goal his clever display deserved with a lob six minutes from the end.