In Singapore, Jordan Henderson and Mohamed Salah scored for the Reds.
Henderson put the Reds in front from Harvey's pull-back, before Salah put the visitors in front early in the second half.
Oxlade-Chamberlain was injured in the first half.
On Tuesday, the Reds were thrashed by Manchester United in Thailand.
It was a routine victory for the Reds at the National Stadium, who last season won the FA Cup and League Cup, came second in the Premier League, and lost in the European Championship final.
Some of the senior players in Palace's squad weren't able to meet the country's entry requirements, while others didn't travel for health reasons.
In the second half, Palace made two blocks of five substitute players, while in the first half, the entire starting 11 was changed.
There were chances for the Reds to record a bigger victory, but they couldn't convert them.
In Austria, Joe Willock, Sean Longstaff and Bruno Guimaraes all found the back of the net in a match between 1860 Munich andNewcastle.
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