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Mourinho was warmly welcomed by Inter, where he won two Serie A titles in just two seasons.
Roma won the league under Jose Mourinho by winning over Fiorentina with two Tammy Abraham assists.
Bartlomiej Dragowski, the England goalkeeper, was sent off for fouling Henrikh Mkhitaryan.
Nicolo Zaniolo was dismissed and Nikola Milenkovic was soon back on track.
Jordan Veretout fired Abraham's cross low and added a third to settle the contest.
Abraham, a former Chelsea player, could have scored a goal but missed the crossbar with a short-range header. The score was still 1-1.
It was a perfect start for Mourinho. The Roma fans were able to make a welcome return by attending the Stadio Olympico's first game since February 2020.
They had to wait for their first two goals to be fully celebrated. Each required VAR checks to determine if Mkhitaryan had been offside prior to finishing the first, and if Abraham had gone too soon to set up the second.
Sunday's match was difficult to judge Mourinho's Roma. The game was complicated by red cards. In the 17th minute Dragowski was sent off for fouling Abraham outside his zone.
The second dismissal occurred in the second period, levelling the scores and rocking Roma enough for them to see their goal advantage erased by Milenkovic. He has been linked with moves to Tottenham and West Ham this season.
Rui Patricio was also signed from Wolves during the off-season. He made a few good saves, but Abraham was the star.
With 20 minutes remaining, he was replaced by cramp but had already shown enough to indicate that he would be an asset to Mourinho during his second spell in Italy.
Mourinho succeeds fellow Portuguese Daniel Fonseca at Roma. He finished seventh in Serie A last year.