Earlier, the two players drew their first and second game in the standard event so they had to play rapid games to decide the winner.
Liem will face Levon Aronian of Armenia in the next round.
By reaching the fourth round of 16 players, Liem will walk away with at least US$ 25,000.
The FIDE World Cup 2019 is a 128-player single-elimination chess tournament held from September 9 to October 4.
The matches from round one to round six consist of two classical games.
The finalists of the tournament will qualify for the Candidates Tournament for the World Chess Championship 2020.
The total prize fund is $1.6 million, with the winner taking away US$ 110,000.