The hosts, who last week benefited from Mauricio Pinilla's stoppage-time goal in their draw with Fiorentina, looked on course for victory when Albin Ekdal put them ahead midway through the first half.
And even though Manolo Gabbiadini equalised at the death, Daniele Conti gave Cagliari the lead again immediately after before De Silvestri popped up in the third minute of time added on and ensure the match finished as a 2-2 draw.
It was the visitors who started brightly with Pedro Obiang shooting narrowly wide in the opening seconds.
But the hosts started to get on top as the half wore on, with Pinilla missing the target from point-blank range and Marco Sau then firing over from a decent position.
The pressure told in the 26th minute when Pinilla played in Ekdal, who went through on goal and slotted past Samp goalkeeper Angelo Da Costa.
Pawel Wszolek thought he had equalised when he had the ball in the back of the net after converting from Davide Gavazzi's cross but the Poland winger was flagged offside.
It was all Cagliari in the second half, with Radja Nainggolan and Ekdal narrowly missing the target from distance, while the former saw another long-range effort well saved by Da Costa, who then denied Pinilla shortly after.
But the Rossoblu were hit with a sucker punch in the first minute of injury time when Gabbiadini's shot trickled through Cagliari keeper Michael Agazzi's arms.
They deservedly re-established their lead through Conti's free-kick from just outside the area, but there was another twist in the tale to come as Samp levelled.
Gianluca Sansone's free-kick into the area caused a scramble, with De Silvestri prodding the ball home and ensure the spoils were shared.