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Senegal's Boulaye Dia opened the scoring four minutes before half-time, firing home to punish Boualem Khoukhi's attempted clearance.
Former Bristol City striker Famara Diedhiou climbed the highest to turn home a splendid header just three minutes after the interval, putting the African champions two goals to the good.
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There were chances for both Watford forward Ismaila Sarr, who was making his 50th cap for his country, and Everton's Idrissa Gueye, but both fired wide of the target.
Qatar's Akram Afif later went down under a challenge from Sarr in the penalty area, but Spanish referee Antonio Lahoz waved play on.
Mendy, who came in for some criticism during Senegal's first match, and has been dropped to the bench by Chelsea boss Graham Potter in place of Kepa Arrizabalaga, made several stunning saves.
He denied Almoez Ali and Ismaeel Mohammad but was unable prevent Mohammed Muntari's powerful header on 78 minutes.
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The hosts went in search of an equaliser, but Bamba Dieng struck late on to ensure Qatar remain bottom of the group after two matches played.
Senegal, following the win, become the first African team to secure a victory at this World Cup.