Gabriel Boschilia opened the scoring from a free-kick before Germain added two more of his own as Monaco put the game to bed before half-time, with substitute Guido Carrillo putting the gloss on the result at the death.
The result comes four days after Monaco beat Tottenham Hotspur 2-1 to secure qualification for the last 16 as winners of their Champions League group.
It was a fifth straight win in all competitions for Monaco and Europe's most prolific side kept up their remarkable scoring record -- they are banging in the goals at an average of just over three per game in Ligue 1 this season.
Leonardo Jardim's men go provisionally top of the table on goal difference from Cote d'Azur rivals Nice, who can move back to the summit when they host Bastia on Sunday.
Defending champions Paris Saint-Germain can also move level on points with Monaco if they win away to Lyon on Sunday evening.
"As coach I'm happy, but the merit goes to the players. They understand, and especially the younger ones, that the difference between the big teams and small ones is the intensity put into matches," said Portuguese coach Jardim, who played down talk of a first title for the club since 2000.
"One match can change everything. We are an ambitious team and we play every game to win it. We will not limit our ambitions, but we have not built a team for the title."
Monaco's starting line-up showed just two changes to the team that had dispatched Spurs at the same Stade Louis II on Tuesday, with Boschilia and Andrea Raggi coming in for Thomas Lemar and the injured Benjamin Mendy.
Brazilian prospect Boschilia opened the scoring midway through the first half when he curled a superb free-kick on his left foot beyond the reach of Yohann Pele and into the top-right corner of the net for his fourth goal of the season.
Germain, whose father Bruno played for Marseille two decades ago, doubled the home side's lead when he headed in after a brilliant Bernardo Silva assist.
And Germain struck again six minutes from half-time, curling a shot beyond the reach of Pele after good play down the right by Djibril Sidibe.
A shell-shocked Marseille, with their new American owner Frank McCourt watching on, had no answer and Monaco secured their record win over OM when they netted again in injury time.
Pele stretched to keep out a Germain chip, but Argentine striker Carrillo, who had replaced Radamel Falcao, converted the rebound to make it four.
Marseille have won just once, and scored just twice, in five league games under new coach Rudi Garcia and remain in mid-table.
Bordeaux are sixth after making it six league games without defeat as Guinea forward Francois Kamano scored two late goals to secure a 3-2 win at home to Dijon.
They are behind Guingamp in fifth on goal difference with the Bretons coming from behind to draw 1-1 at Caen thanks to Nill De Pauw's late leveller.
Bottom club Lorient threw away a two-goal lead to draw 3-3 at Metz while Montpellier's meeting with Nancy ended goalless, as did the encounter between Nantes and managerless Lille.