Seeking their first pre-season victory after draws with Thailand and Swiss side St Gallen and a 1-0 loss to Rapid Vienna, the Reds gave a disjointed appearance in the first half but took the lead with the final kick before half-time when Andriy Voronin's long-range effort found the net.
Albert Riera extended the advantage early in the second half before Nemeth struck twice in the final 17 minutes with a Fernando Torres effort wedged in between.
With Rafael Benitez including a number of unfamiliar faces including goalkeeper Diego Cavalieri, defenders Mikel Dominguez and Philipp Degen and forward David Ngog in his starting line-up, the Reds struggled to assert themselves in the first half against a defensively-minded Singapore side.
Ryan Babel rose above the Singapore defence to put a header straight at goalkeeper Hassan Sunny after seven minutes but apart from that, there was little to entertain the crowd in the first half as the Premier League side were restricted to shots from distance.
There were some moments of concern for the Reds as Javier Mascherano twice went to ground after heavy challenges by Mustafic Fahrudin and Noh Alam Shah and the hosts nearly took a shock lead in the 22nd minute when Shi Jiayi's through pass released Shahril Ishak whose weak shot was easily saved by Cavalieri.
But in stoppage time at the end of the half, Liverpool's opening goal arrived from out of the blue as Voronin got past the challenge of Fahrudin and, with the Singapore defence backing off, fired in an innocuous low shot that crept past a late-diving Hassan.
Buoyed by the unexpected goal, Liverpool were much improved after the break and extended their lead 10 minutes into the second half when Mascharano floated in a fine cross from the right for Riera, who chested the ball down at the far post before firing a low shot past Hassan.
The fans were clamouring for an appearance by Torres and got their wish just after the hour when he was brought on with Dirk Kuyt in place of Yossi Benayoun and Ngog.
It was the Dutchman that would make the bigger impression though setting up the last three goals, beginning in the 73rd minute when he crossed from the right for 20-year-old Nemeth to slide the ball past Hassan to make it 3-0.
Alonso came on in the 77th minute for Daniel Agger and just three minutes later started the move that ended with Kuyt crossing for an unmarked Torres to apply the finishing touch from point blank range for his first pre-season goal.
And with seven minutes left, another Kuyt cross found Nemeth, who headed home his second of the game.