Midfielder Dimitri Payet was involved in both goals setting up Morgan Sanson for the opener before converting from the penalty spot as Marseille extended their unbeaten run to five.
Villas-Boas kept faith with the side which beat Brest 2-1 on Friday electing against giving match-winner Nemanja Radonjic a spot in the starting lineup.
Angers boss Stephane Moulin made five changes from the weekend's loss to Nice as Ismail Traore took over the captaincy from Thomas Mangani.
In an open first quarter of an hour both outfits had numerous efforts on target including Payet for the visitors and Angelo Fulgini for the hosts.
Villas-Boas' men claimed the lead after 17 minutes as Sanson registered his second goal in four league games.
Payet played his free-kick quickly to find midfielder Sanson who side-footed cooly past Ludovic Butelle.
Payer doubled the advantage after 41 minutes slotting his third penalty of the season.
Japan right-back Hiroki Sakai was tripped up in the Angers box and the France attacker scored his fifth goal of the season.
With 20 minutes to play Moulin brought on centre-back Mateo Pavlovic to partner Sada Thioub up front looking for a way back into the fixture but Marseille held on to move on to 31 points, with PSG on 33.
Crowd trouble in Bordeaux
Elsewhere, Bordeaux's match with Nimes' at the Matmut Atlantique was delayed for 30 minutes during the first half as around 20 home fans invaded the pitch.
The supporters aggrievances were targeted towards club president Frederic Longuepee after being refused from flying a banner at the game calling for his resignation.
Italian Cristian Battocchio scored a hat-trick as Brest moved up to 12th spot with a 5-0 hammering of Strasbourg.
Later Lyon host Lille and on Wednesday PSG can reinstore their five-point lead over Marseille as they welcome Nantes, who have recovered from a run of four straight defeats, to the French capital.