Obbadi opened the scoring for the oil-rich side when he volleyed in from the edge of the box through a ruck of players inside the area just before the half-hour mark.
Ligue 1's top-scorer Falcao ended his 307-minute goal drought nine minutes before the break when he chipped the goalkeeper with a brilliant effort.
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Gomis reduced the deficit just after the hour mark when he headed home a cross from Henri Bedimo, but the strike was merely a consolation as the home side held on to take the points.
The win takes Monaco above PSG by one point.