- Felix Afena-Gyan (82', 90'+4')
Henrikh Mkhitaryan thought he had given Roma the lead in the first half with a thunderous strike, only for the eagle-eyed referee to rule the goal out after spotting a handball from Tammy Abraham as the effort flew past the English striker.
The visitors looked like they were going to have to settle for a frustrating draw going into the latter stages of the match as Andriy Shevchenko's Genoa frustrated their opponents in the new coach's first game in charge.
However, 18-year-old Afena-Gyan had other ideas and he scored in the 82nd minute to edge his side in front, running to celebrate with a jubilant Mourinho after finding the net, before curling a stoppage-time second to seal the win.
The victory, just Roma's second in eight matches in all competitions, moved Mourinho's men up to fifth in the standings, while Genoa stay 18th.