Diego Jota and Roberto Firmino scored 15 minutes into the game to give Liverpool a 2-0 lead over already-relegated Southampton side before James Ward-Prowse halved the deficit four minutes later.
Black Stars winger Kamaldeen Sulemana scored the equalizer for the Saints in the 28th minute as the first half ended in a 2-2 draw.
The Right to Dream Academy graduate bagged his brace quickly after recess to ensure Southampton come from 2 goals down to lead before Armstrong scored to make it 4-2.