The England international, deployed in a forward three alongside Daniel Sturridge and new signing Lazar Markovic at Soldier Field in Chicago, beat goalkeeper Balazs Megyeri with a half-volley on the stretch with just five minutes on the clock and that proved enough in the Reds' Pool B opener.
Gevorg Ghazaryan rewarded the Greek side's rally with a blistering strike four minutes after the restart but could only watch his shot crack the goalframe.
And though Andres Samaris seemed set in stoppage-time to ensure the points were shared, his right-footed effort from just outside the box was knocked away by Brad Jones.
In front of a crowd of 36,170, Brendan Rodgers began with England World Cup quartet Steven Gerrard, Glen Johnson, Sturridge and Sterling, with the latter on the right flank and Markovic on the left.
Jordan Henderson and Emre Can were also included, with Brad Jones, Kolo Toure, Martin Skrtel and Jose Enrique completing the starting line-up.
For the early goal, Gerrard's pass found Sturridge whose scuffed shot was deflected - and the ball fell kindly for Sterling to finish.
After the impressive Markovic had fired a shot over the crossbar, Enrique needed to be alert to make an important tackle to deny Javier Saviola, who had earlier been booked for diving.
Markovic was replaced by Philippe Coutinho at the break, while Sturridge completed 75 minutes and also claimed the man-of-the-match award.
Coutinho almost doubled the Reds' advantage in the closing stages but his 25-yard effort went just wide.
There was still time for centre-back Sebastian Coates to save the blushes of fellow substitute Joe Allen after the Welshman had allowed Andreas Bouchalakis to steal the ball, while Jones was forced into a fine late save by Megyeri.
Afterwards, Rodgers told reporters: "The passing was crisp and precise. We scored a very good goal and looked a real threat at the top end of the field.
"But I was also very pleased with how we defended.
"I was delighted with the team. As pre-season goes on, we will be getting sharper in our movements and passing, but at this moment it is about building up the resistance of the players and getting minutes under their belt."
Liverpool will next face Manchester City, the side that pipped them to the Premier League title last term by two points, on Wednesday night at New York's Yankee Stadium.
Watch Liverpool v Manchester City live in the International Champions Cup on Sky Sports 1 HD (kick-off 12am BST on Thursday, July 31).