Marcelo Bielsa's side have now won five games in a row after picking up one point from their first two games and are still yet to suffer defeat on the road in 2014-15.
Andre-Pierre Gignac started the match as the league's top goalscorer with six in six games and he had a chance to make it seven when the visitors were awarded a penalty in the seventh minute.
His spot kick came back off the post, but he made up for the miss instantly by heading home Benjamin Mendy's cross from the left as Marseille came straight back on the attack.
Ayew then joined Gignac on a brace with an inventive 'rabona' finish from close range just before the hour mark.
Giannelli Imbula completed the rout by arrowing a low 25-yard drive into the far corner after shifting the ball onto his left foot.
Marseille's win ends a run of two straight victories for Reims, who are now 17th in the table.