Coutinho got the Reds going with a 10th-minute opener and Sterling sealed the win two minutes from time as Brendan Rodgers' men prepared to go to Australia to face Melbourne Victory on Wednesday.
They will then round off their tour with a game in Thailand on July 28 before beginning their Barclays Premier League campaign against Stoke on August 17.
Coutinho opened the scoring as he attempted to find new signing Luis Alberto but the ball ended up back at his feet, allowing the Brazilian to slot home underneath goalkeeper Kurnia Meiga.
Stewart Downing then brought a save out of the stopper before Alberto hit the post.
And he was not to be the only newcomer to trouble the woodwork as Iago Aspas hit the bar before the break.
Simon Mignolet did well to save a long-range effort from Sergio Van Dijk but the Reds should have gone two up as Coutinho put a great chance over the bar.
Multiple substitutions came in the last half-hour and Sterling hit the bar twice soon after being introduced.
But he was not to be denied in the 88th minute as he side-footed into an empty net after some good work from Oussama Assaidi and Jordon Ibe.