Sampdoria rewarded coach Marco Giampaolo with a new contract in midweek after his side had ended Inter Milan's bid for Champions League football next season with a shock 2-1 win at the San Siro.
But despite taking a 2-1 lead at the Luigi Ferraris stadium thanks to Ricky Alvarez's 71st minute strike, Sampdoria were pegged back on the stroke of full-time and lucky to escape with a point after goalkeeper Emiliano Viviano stuck his leg out to thwart Babacar's last-gasp effort at the far post.
Samp welcomed Paulo Sousa's men to the Luigi Ferraris brimming with confidence after their credible away win last week.
Fiorentina came close to levelling when Federico Bernardeschi's free kick curled inches wide.
But a blunder from Tatarusanu, whose goalkick was straight to Patrik Schick, forced the Romanian goalkeeper to scramble to parry Fernandes' effort from point-blank range.
Babacar fired an audacious lob off target, and Fiorentina spurned the chance for a first-half leveller when Carlos Sanchez turned a free header over the bar from a corner.
Kalinic came off the bench to replace Josip Ilicic for the second half, but a more enterprising Fiorentina were wasteful.
Some fancy footwork from Tello took the Spaniard past Dodo on the right flank but the Spaniard's low angled drive came back off the base of the far upright.
Tello beat the Brazilian again to deliver for Babacar, whose drive was blocked by Matias Silvestre.
Fiorentina finally pulled level on the hour when Gonzalo Rodrigues rose at a corner to glance a header past life-long Fiorentina fan Vivivano.
But on a Samp counter Alvarez was given acres of space on the left to fire Quagliarella's delivery past Tatarusanu on 71 minutes.
Fiorentina should have levelled immediately but Kalinic made a mess of Tello's cross, before hitting the post with a header from the Spaniard's perfect delivery on 79 minutes.
But Fiorentina were building momentum and were rewarded in the dying minutes when Babacar coolly collected on the edge of the area to lob Viviano in the 89th minute.
The Senegal striker could have snatched all three points in the dying seconds but saw Viviano stick out his left leg to thwart his drive from the left flank.
Fiorentina remaining eighth, seven points off Atalanta in the first Europa League spot, with Samp seven points behind in ninth place.