Brendan Rodgers' men were buoyed to victory by a fifth-minute goal to Raheem Sterling, who benefitted from a deflected shot from strike partner Daniel Sturridge.
The Reds were good value for their win, although Olympiacos were inches away from earning a point, with Gevorg Ghazaryan denied by the crossbar early in the second half with Brad Jones beaten.
Liverpool's first match of the pre-season tournament in the US saw them start well, with a free-kick in the fourth minute in a dangerous area, before they took the lead a minute later.
Sturridge's attempt from distance deflected off an Olympiacos defender, and fell fortunately to Sterling, who tucked away past a helpless Balazs Megyeri.
However, it was Olympiacos who should have struck first on return to the Soldier Field playing arena, as Ghazaryan's shot was agonisingly denied by the woodwork.
Andreas Bouchalakis then had a gilt-edged chance to equalise, forcing a turnover deep in Liverpool's defensive third, however he could not control his final touch around goalkeeper Jones as the chance dissipated.
