The win lifted Marseille above their visitors and into fourth place.
Mercurial striker Balotelli held off Loic Perrin and twisted his body to volley the ball home from a corner in the 12th minute, before he celebrated by grabbing a mobile phone from a photographer in the Stade Velodrome to record a selfie of the moment.
Thauvin struck the second from the spot nine minutes later after a handball by Mathieu Debuchy to seal a straight-forward win.
Marseille have 44 points, one more than Saint-Etienne, and five adrift of the Champions League spots.
Earlier on Sunday, Lyon forward Moussa Dembele struck two second-half goals to round off a thumping 5-1 win over visitors Toulouse at the Groupama Stadium.
Memphis Depay opened the scoring for the third-placed hosts on 10 minutes but the lead was short lived as Matthieu Dossevi put Toulouse back on level terms five minutes later.
Bertrand Traore restored Lyon’s lead with a bizarre goal on the half-hour, whipping a left-foot effort into the danger area that goalkeeper Baptiste Reynet allowed to fly past him.
Lyon increased their advantage five minutes later when Nabil Fekir won a penalty which he fired home himself and Dembele’s double put the icing on the cake.
Lyon are now five points behind second-placed Lille, who won 1-0 at home to Dijon, and 22 adrift of runaway leaders Paris Saint-Germain, who have 71 points.
Seventh-placed Nice beat Strasbourg 1-0 courtesy of a Youcef Atal goal on 20 minutes.
Nice’s Danilo and Strasbourg’s Samuel Grandsir were both sent off after an ugly 89th minute confrontation.
Bottom side Guingamp secured a point with a scoreless draw at home with Nantes.
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