Match highlights (UK only)
Having beaten Guangdong 4-3 in China three days ago, there were nine more goals in an entertaining clash against a Malaysian XI.
Adam was a lively presence in the opening exchanges and after 25 minutes played in Carroll, who went down in the area and earned the penalty.
Adam had to take the spot-kick twice but sent the keeper the wrong way to make it 1-0.
Mohammad Safiq Rahim equalised with a fine free-kick five minutes from half-time.
Liverpool made 11 substitutions at the break and after 68 minutes David Ngog scored following some poor defending.
The Frenchman added a second moments later with a thunderbolt finish.
Maxi Rodriguez made it 4-1 in the 76th minute before Mohammad Safi scored twice in as many minutes to put the hosts back in contention.
Maxi then scored a second of his own in the last minute of the 90 as the All-Stars chased the equaliser. And Dirk Kuyt netted the sixth when bursting through to slam home.