City took the lead with just three minutes on the clock when debutant Raheem Sterling broke free of the Roma defence before calmly slotting past Morgan De Sanctis.

Raheem Sterling of Manchester City celebrates scoring in the International Champions Cup on July 21, 2015 © Getty Images

However, the Italians drew level five minutes later as Miralem Pjanic beat Wilfredo Caballero with a powerful drive from 25 yards that flew into the top corner.

Chances continued to arrive during the remainder of what was an entertaining opening half, with David Silva and Kelechi Iheanacho both being denied by De Sanctis.

The lively Iheanacho came close to giving Manuel Pellegrini's side the lead on 34 minutes when he jumped highest to meet a cross from Silva, but De Sanctis was alert to the danger again and parried the ball away.

Miralem Pjanic of AS Roma celebrates with team-mates after scoring a goal during the International Champions Cup friendly match between Manchester City and AS Roma at the Melbourne Cricket Ground on July 21, 2015 © Getty Images

Roma enjoyed a strong finish to the half after struggling to create opportunities in front of goal, but they failed to make their late dominance count. The closest that they came was from a corner, but Daniele De Rossi could not keep his header down.

A busy start to the second half saw City go back in front on 51 minutes through Iheanacho, who capitalised on some sloppy defending to rifle the ball into the net.

The Premier League side pushed hard for a third soon after as Jesus Navas fired over before De Sanctis kept out Marcos Lopes with an instinctive save. Yaya Toure then tried his luck with a fizzing strike, but substitute goalkeeper Bogdan Lobont was there to keep it out.

Kelechi Iheanacho of Manchester City is congratulated by teammates after scoring a goal at the International Champions Cup football match between English Premier League team Manchester City and Italian side AS Roma in Melbourne on July 21, 2015 © Getty Images

City were made to pay for those misses with just two minutes remaining when Adem Ljajic curled in a free kick from the edge of the box following Toure's foul on Seydou Doumbia.

With the game going to penalties, Aleksandar Kolarov's missed effort looked to be decisive as Doumbia stepped up to win the match for Roma. However, his spot kick was saved by Joe Hart before the England international kept out Seydou Keita's penalty to win the match for City.