Serbia-based Richmond Boakye bagged a brace as the Black Stars achieved their biggest away winning margin in an eliminator since a 4-0 triumph over Cape Verde 12 years ago.
The crucial goal came two minutes into first-half stoppage time when Partey ran on to a pass and rifled a right-foot shot past goalkeeper Barel Mouko from a tight angle.
It gave Ghana a 3-1 half-time advantage and the lead was rarely threatened in the second half as Congo slumped to a record home defeat in a World Cup qualifier.
Ghana coasted to maximum points despite lacking two injured stalwarts, West Ham United midfielder Andre Ayew and Turkey-based striker Asamoah Gyan.
The three-time World Cup qualifiers hope second-place Egypt and leaders Uganda draw later Tuesday before an expected 70,000 crowd in Mediterranean city Alexandria.
Uganda have seven points and Egypt six, and Ghana five having played one match more, with only the group winners qualifying for the 2018 World Cup in Russia.