The build-up to the match in Melbourne was predictably dominated by City's new record signing, and he delivered immediately with a cool finish.
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But, after stunning strikes from Miralem Pjanic and Adem Ljajic sandwiched a goal from City's Kelechi Iheanacho, the English Premier League side needed penalties to win.
Joe Hart delivered in the shootout, scoring his own spot-kick before saving Seydou Doumbia and Seydou Keita's efforts to give City a 5-4 victory.
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Welcomed to the pitch at the MCG by a chorus of boos, Sterling provided those hoping he would fail in a sky blue shirt with some ammunition when he slipped over inside the opening minute.
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But soon after, the 20 year-old showed why City was so keen to secure his signature, as he slotted calmly into the bottom-right corner in a one-on-one with Morgan De Sanctis after being played in by Iheanacho.
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Roma levelled eight minutes in, as Pjanic unleashed a long-range rocket that gave Willy Caballero no chance, before David Silva - central to most of City's best moments before he was withdrawn at the interval - forced De Sanctis into a top save
Sterling was regularly in the spotlight in the first half, and the former Liverpool man had a clear penalty turned down in the 23rd minute when he was tripped by Alessandro Florenzi having expertly shimmied past the Roma full-back.
Silva also picked out Iheanacho in the 33rd minute but the latter's header was straight at De Sanctis before Roma finished the half stronger - two cut-backs forcing desperate clearances before Daniele De Rossi's header went just over the bar.
Inevitably, the second half barely got going due to a raft of substitutions from both coaches.
But it was City which hit the front early in the second period, as Iheanacho got the goal his performance deserved, with former Chelsea and Arsenal full-back Ashley Cole inadvertently providing the assist.
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Cole chipped team-mate Mapou Yanga-Mbiwa with his back-pass and Iheanacho took advantage, firing past De Sanctis in the 51st minute.
The relatively sparse crowd inside the cavernous MCG had to wait until the 87th minute for another goal, with Ljajic beating Hart from 20 yards from a free-kick, before the England goalkeeper decided the contest in the shootout.
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