The Giallorossi got back to winning ways in the most dramatic fashion possible, having seen ex-academy player Daniele Verde equalise for the visitors in the final moments of normal time.
But, with only seconds remaining, substitute Bruno Peres squared for Pellegrini to rifle home - ensuring something of a nightmare week ended on a positive note.
It was clearly a relief to the captain for the day, as he ran to the corner flag and celebrated wildly with his teammates.
Looking to avenge the midweek Coppa Italia exit at the hands of the same opposition, Paulo Fonseca's side twice took the lead through Borja Mayoral - with Roberto Piccoli's tap-in splitting the two.
When Rick Karsdorp then slid home his first goal for the club it looked like Roma were on their way to a massive three points; only for Diego Farias to find the net and half the deficit with 30 minutes still to play.
When Verde then took advantage of a mistake to fire home an equaliser in the 90th minute, it looked like a difficult week was about to get even worse.
Until Pellegrini stepped up, that is, and marked his 100th Serie A appearance with a vital strike from inside the box.
ROMA 4-3 SPEZIA
SCORERS: Mayoral (17', 52'), Karsdorp (55'), Pellegrini (90'+2); Piccoli (24'), Farias (58'), Verde (90')
ROMA (3-4-1-2): Pau Lopez; Ibanez, Smalling, Kumbulla; Karsdorp (Peres), Veretout, Villar (Cristante), Spinazzola; Pellegrini, Perez (Diawara); Mayoral
Unused subs: Farelli, Fuzato, Santon, Diawara, Darboe, Feratovic, Providence, Tall, Pogdoreanu
SPEZIA (4-3-3): Provedel; Dell'Orco (Bastoni), Chabot (Erlic), Terzi, Marchizza; Estevez, Agoumé, Maggiore (Acampora); Gyasi (Verde), Piccoli (Galabinov), Farias
Unused subs: Krapikas, Ramos, Ricci, Pobega, Deiola, Ismajli, Agudelo
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