Murray's win on the clay court came during a steady rain that prompted Djokovic to make a plea to halt the match.
The victory came on Murray's 29th birthday.
"The finals of a Masters series on clay is something that's a new experience for me," Murray said afterward. "It's nice to still be sort of achieving new things and reaching new goals at this stage of my career."
Murray avenged last week's championship-match loss to Djokovic at the Madrid Open.
The title is Murray's first in Rome and he joined Pat Hughes (1931) as the other British men to win the Italian Open
"It's mostly great players have won this event," Murray said. "So I'm very proud to have my name on the trophy."
Djokovic had beaten Murray in 12 of their past 13 matches prior to Sunday's loss.
The Serbian loudly complained about the conditions during the first set but the umpire allowed the match to continue. Djokovic argued again for a stoppage when he nearly slipped during the second set.
"I didn't ask to postpone the match," Djokovic said afterward. "I asked to have a little break where we would give a little more time, maybe five more minutes, to people to arrange the court."
Djokovic wasn't at his best as he dealt with a sore left ankle after had played tough matches with Rafael Nadal and Kei Nishikori during the week.
"It was a week with a lot of emotions, a lot of hours on the court," Djokovic said. "It wasn't easy to be fresh today and have the strength to play with Andy. He was just too good today and he deserved it."