Qatar are on the verge of a group-stage exit in their home World Cup after suffering a second successive defeat against Senegal.
The Middle East side battled valiantly but will be out with a game to spare if the Netherlands avoid defeat against Ecuador later on Friday (16:00 GMT kick-off).
But the African champions are up and running courtesy of Boulaye Dia breaking the deadlock four minutes before half-time, slamming home to punish Boualem Khoukhi's miscued clearance.
Looking to hit back in the second period, Qatar's hopes were dashed when former Bristol City striker Famara Diedhiou rose to flick in a glorious header just three minutes after the break.
Watford's Ismaila Sarr had an early chance on his 50th cap but struck into the side netting, while Everton's Idrissa Gueye's rasping drive went narrowly wide.
Qatar felt they should have had a first-half penalty when Akram Afif was bundled over in the box by Sarr, but Spanish referee Antonio Lahoz pointed only for a goal-kick, much to the anger of the home supporters.
Chelsea goalkeeper Edouard Mendy made stunning reflex saves to deny Almoez Ali and Ismaeel Mohammad but he could do nothing about Mohammed Muntari's powerful header.
Qatar were searching for the equaliser, but Bamba Dieng stroked in to deflate the home following and leave Qatar bottom of the group without a point after two games played.
