Having completed his £49million move from Liverpool last week, the 20-year-old did not take long to make an impact for his new club as he slid a shot past Morgan De Sanctis with just 137 seconds on the clock.
Miralem Pjanic replied with a well-struck equaliser, but Sterling continued to impress at the Melbourne Cricket Ground until he was replaced at half-time.
City regained the lead when Kelechi Iheanacho capitalised on Ashley Cole’s poor backpass to score, only for a brilliant late free-kick from Adem Ljajic to level at 2-2 and force penalties.
Roma took an early advantage after Aleksandar Kolarov missed, but Joe Hart saved two penalties and scored one to secure a 5-4 victory for City.
While last season’s Premier League runners-up fielded a number of youngsters at the MCG, all eyes were on Sterling in his first appearance for City.
Playing in the number seven shirt, his first touch is one he will want to forget as he fell over the ball – much to the delight of the Liverpool supporters in the stadium.
However, that was soon forgotten as the England international raced on to Iheanacho’s through ball in the third minute and calmly finished past De Sanctis.
Roma were back on level terms just minutes later when Pjanic rifled a 25-yard shot past Willy Caballero and into the back of the net.
Sterling thought he should have had a penalty to add to his goal when he was brought down by Alessandro Florenzi midway through the first half, but the referee waved play on.
Roma, who finished second in Serie A last season, finished the half on top as Vincent Kompany and Eliaquim Mangala cut out dangerous crosses with players waiting in the middle.
Sterling’s last action of his debut was to fire a long-range effort over the bar before he was one of nine City changes at the break.
One of Roma’s half-time substitutes, Cole, gifted City their second goal soon after the interval when he headed into Iheanacho’s path and the Nigerian youngster finished the one-on-one chance.
Rony Lopes was then denied from close range by De Sanctis before Yaya Toure fired in a first-time shot that the keeper did well to hold.
It looked as though City would hold onto their advantage until the 87th minute when Toure gave away a free-kick on the edge of the box and Ljajic fired past Joe Hart.
That took the game to penalties and it looked as though Roma would come out on top as Kolarov blazed City’s second attempt over the bar.
However, after scoring a spot-kick, Hart saved Seydou Doumbia’s chipped effort and then kept out Seydou Keita’s shot to ensure City triumphed.