The African champions needed a win against their South American opponents to be sure of advancing to the next stage of the tournament and found themselves 1-0 up at half time thanks to Ismaila Sarr's penalty.
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It appeared Senegalese hearts were being broken midway through the second half when Moises Caicedo netted the equaliser from close range following a well-worked corner.
But on 70 minutes Koulibaly volleyed Senegal back in front as he took advantage of Ecuador's inability to clear a free-kick from the Lions of Taranga.
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On his 67th cap, this was Koulibaly's first goal for his country and talkSPORT's Perry Groves was very impressed with the improvisation of the Chelsea centre-back.
Commenting on Kouliably's finish, Groves said: "A goal Harry Kane would've been proud of."
The result means Senegal finish second in Group A with the Netherlands topping the group thanks to a convincing 2-0 win over Qatar.
It also means Senegal could play England in the Round of 16 at the World Cup, with the runners-up of Group A taking on the winners of Group B.
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The Round of 16 match will take place on Sunday at 7pm at the Al Bayt Stadium.