The 20-year-old was jeered at the Melbourne Cricket Ground when he tripped over the ball on one of his first touches in the area, but a minute later soaked up the acclaim after slotting home a through ball from Nigerian teenager Kelechi Iheanacho.
Though all eyes were on Sterling, the most expensive English player in history after joining from Liverpool for a reported 49 million pounds, it was goalkeeper Joe Hart who secured victory with two fine saves in the shootout as City prevailed 5-4 on spot-kicks after the teams drew 2-2.
Aleksandar Kolarov missed City's second kick in the shootout but Hart parried away a weak effort from Seydou Doumbia and also denied Seydou Keita to clinch the International Champions Cup victory in front of a crowd of 41,134.
Sterling's transfer fee generated plenty of debate, but his man-of-the-match performance against the Serie A side was a positive start in justifying his price-tag.
He was desperately unlucky not to create a second goal before being substituted at halftime, garnering no sympathy from Australian referee Jarred Gillett despite a forceful challenge from Alessandro Florenzi that took out the Englishman's legs.
Roma forward Adem Ljajic curled in a sumptuous free kick three minutes from full-time after being brought down just outside the area to take the match into the shootout.
Eighteen-year-old Iheanacho, a much-hyped product of City's youth academy, also impressed with his calm in front of goal, hammering home City's second in the 51st minute after being gifted the chance when a defensive pass intended for keeper Morgan de Sanctis landed horribly short.
Miralem Pjanic scored Roma's first in the eighth minute with a thundering 25-metre strike.
