Second-placed Marseille are seven points adrift of reigning champions PSG, who visit last year's runners-up Lille on Sunday.
The hosts rarely threatened against a solid Angers outfit at the Stade Velodrome, but did extend their unbeaten run in all competitions to 12 matches.
Villas-Boas defended his side when asked if they rely too much on star Dimitri Payet, who missed the game through suspension.
"With 11 guys behind the ball, where do you want us to go? You need dribbling, winning duels, finding the last pass or goal and Payet does just that," said the Portuguese coach.
"But Barcelona are (Lionel) Messi-dependent, Juve are (Cristiano) Ronaldo-dependent. If we are Payet-dependent, I have no problem with that."
Nemanja Radonjic fired narrowly wide for Marseille on the stroke of half-time, while the away side almost snatched a 90th-minute winner when Antonin Bobichon's effort flew over.
But Angers failed to muster a single shot on target, with their opponents managing just two.
Marseille sit five points clear of Rennes in the race for automatic qualification for next season's Champions League group stage, after the third-placed side were held to a 1-1 draw at Nice on Friday.
Elsewhere on Saturday, Monaco slipped to a 3-1 home defeat by Strasbourg to leave new coach Robert Moreno still waiting for a first Ligue 1 win after three matches.
The principality club, who drew 3-3 with PSG before being thrashed 4-1 by the champions in former Spain boss Moreno's first two league games, sit 12th in the table and eight points behind Rennes.
Montpellier edged out struggling Dijon 2-1 to move into fourth, while former Sunderland winger Wahbi Khazri scored twice in Saint-Etienne's 2-1 win over Nimes.