Samp were targeting the top half of the Serie A table after winning their last two games while Fiorentina still hope to chase down third-placed Napoli and snatch the last Champions League place.
Manolo Gabbiadini and Eder might have won it for Sinisa Mihajlovic's hosts and La Viola spurned several late chances to bag all three points - Borja Valero and Alessandro Matri proving particularly wasteful in Genoa.
There were several flashes of real inspiration in a lively first half and Eder's control-and-shot on six minutes got the Marassi crowd buzzing.
He then forced a save from Fiorentina goalkeeper Neto before Valero tried his luck at the other end.
Gabbiadini came closest to firing Samp ahead before the break with a searing free-kick that skipped over the wall and sent Neto sprawling to make the save.
Fiorentina bit back but, despite the best efforts of Juan Cuadrado in providing the killer pass, Mati Fernandez's close-range finish fizzed just wide.
Samp looked much improved when play resumed and Gabbiadini soon worked Neto again after streaking into the box from the right wing.
Maxi Lopez collected Roberto Soriano's pass to drive the ball at Neto and, in the 65th minute, Angelo Palombo's long-range effort whistled past a post.
Fiorentina found themselves restricted to long shots for much of the second half and Valero tried to make the most of the situation when noticing Angelo Da Costa off his line in the 73rd minute.
The Samp defence recovered the ball, though, and raced upfield to rattle Neto with two quickfire efforts from Soriano.
As time ticked away Juan Manuel Vargas steered a swerving free-kick over the wall, but wide, and Massimo Ambrosini headed Valero's cross into Da Costa's gloves.
Fiorentina should have nicked it at the death when Matri rose to meet Valero's free-kick with his head, but the ball bounced out of play.
Samp boss Mihajlovic should have been delighted with the late let-off, yet he was instead ordered from the touchline for arguing with an official in the moments before the final whistle.