Germain got his first goal on 11 minutes with a powerful close-range header following a corner. After Saint-Etienne defender Ronael Pierre-Gabriel was sent off in the 51st, Germain grabbed his second in the 71st when he turned in winger Florian Thauvin's cross.
"Of course I was waiting for this, to score in the league. Or to score at all because I hadn't scored for three months," Germain said on French television. "But I never lost confidence in myself. I hope this match helps me to play more regularly."
Argentine winger Lucas Ocampos expertly curled in the third goal from just inside the penalty area late on. Marseille remains in fourth place, level on points with Monaco and Lyon but trailing them on goal difference. They are nine points behind runaway leader Paris Saint-Germain. Saint-Etienne is down in 15th spot.
PSG and Monaco won their games on Saturday.
Days after being linked with a potential move to Barcelona, teenage midfielder Houssem Aouar scored twice as Lyon rallied to win 2-1 at Amiens.
He started and finished the move that drew Lyon level in the 79th and volleyed in the winner four minutes into injury time.
The 19-year-old Aouar is the latest young talent to come through Lyon's prodigious youth academy, and was recently supervised by Barcelona. His astute passing, and skill and composure on the ball reportedly pleased the Catalan giant.
Over the years, Lyon's academy has given young players the chance to shine by bringing them into the senior team quickly. It has produced Real Madrid star Karim Benzema, Arsenal striker Alexandre Lacazette and Nabil Fekir, the club's top scorer this season and another player widely tipped to move to a bigger club in the summer.
Amiens scored in the ninth minute through forward Serge Gakpe's close-range finish.
Lyon thought it had equalized in the 18th but forward Memphis Depay's free kick was ruled out for an offside teammate.
Aouar's equalizer was reward for his perseverance and talent.
Coming in from the left, he beat two players, fed a pass to midfielder Tanguy Ndombele and then sprinted to slide home Ndombele's pass across the penalty area.
After Amiens forward Gael Kakuta hit the post with a penalty, Aouar's winner sparked scenes of jubilation.
Striker Mariano Diaz burst into the area and, rather than shooting, cleverly sent a looping pass toward the left post where Aouar volleyed the ball neatly into the right corner.
Mario Balotelli's cushioned volley from the edge of the penalty area gave Nice a 2-1 win at fifth-place Nantes.
The Italian striker had just missed a more straightforward chance when he sent a first-time volley into the bottom right corner in the 75th minute, with speedy winger Allan Saint-Maximin again the provider.
It was Balotelli's ninth goal in 12 league games and prompted one fan to sprint onto the field to congratulate him. The match was briefly held up while security staff wrestled the intruder to the ground and then removed him.
Nice was indebted to goalkeeper Walter Benitez's stunning point-blank save from Jules Iloki's header just after Balotelli's goal.
Forward Yacine Bammou put Nantes ahead in the 12th minute. Striker Alassane Plea headed the equalizer close to halftime.
Following a terrible start to the season, Nice is up to eighth place.