After suffering a defeat in the 1984 European Cup final and missing out on UEFA Cup glory seven years later, the Serie A side was not to be denied an elusive European triumph and lifted its first trophy since the Coppa Italia in 2008.
Zaniolo, who missed the entire 2020-2021 season after suffering a second ACL injury in under a year, dinked in an exemplary finish in the 32nd minute to put Roma in charge.
Feyenoord upped its game after the restart and was denied by the woodwork twice in three minutes, but Jose Mourinho's men tightened up and saw out a famous victory.
The meeting between the competition's two most prolific sides was bereft of goalmouth action for much of the first half, with Henrikh Mkhitaryan's withdrawal due to injury the most notable event in the opening half hour.
Roma moved in front with the first real chance of the match, though, as Zaniolo brought down Gianluca Mancini's excellent delivery with his chest and stabbed an instinctive finish home.
Feyenoord made a bright start to the second half and Mancini diverted a fizzed low cross onto the near post of his own goal before Rui Patricio parried Guus Til's follow-up behind.
Patricio produced a stunning stop in the 50th minute when he tipped a ferocious 20-yard drive from Tyrell Malacia onto the woodwork.
Justin Bijlow denied Jordan Veretout and Lorenzo Pellegrini as Roma tried to get a second on the break, but Bryan Linssen was unable to connect with Cyriel Dessers' flick-on in stoppage time on a painful evening for Feyenoord.