Pellegrini converted from 12 yards out deep into injury time to rescue a point at the Stadio Friuli, in a game where Roma seemed destined for large parts to come away with nothing.
A late flurry from Jose Mourinho's side gave the visitors hope, however - and an eventual penalty from Marvin Zegelaar gave Pellegrini the chance to continue Roma's unbeaten streak.
Nahuel Molina gave Udinese the lead early on with a powerful strike from the edge of the box, although the hosts squandered further opportunities to extend that advantage - with Rui Patricio making a handful of important interventions.
Only in the second half did Roma really spark into life, with Udinese goalkeeper Marco Silvestri and some resolute defending combining to deny the Giallorossi an equaliser.
That was, at least, until Pellegrini was given a gilt-edged late chance to level things up.
Roma's next league encounter is the derby against Lazio on Sunday - prior to that they have the small matter of the UEFA Europa Conference League last-16 second leg against Vitesse Arnhem at the Stadio Olimpico to negotiate.
UDINESE 1-1 ROMA
SCORERS: Molina (15'), Pellegrini (90')
UDINESE (3-5-2): Silvestri; Becao, Pablo Marí, Perez; Molina, Pereyra, Jajalo, Makengo (Samardzic), Udogie; Beto, Deulofeu (Pussetto)
ROMA (3-4-1-2): Rui Patricio; Mancini (Perez), Smalling, Ibanez; Karsdorp (Veretout), Sergio Oliveira (El Shaarawy), Cristante, Zalewski (Afena Gyan); Pellegrini; Zaniolo, Abraham (Shomurodov)
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