Mohammed Muntari made history as the first Qatari player to score at the World Cup, but it wasn't enough as Senegal's class told in the end.
After suffering 2-0 defeats in their opening games, both teams faced a virtually do-or-die situation at Al Thumama Stadium.
But you wouldn't have known it judging by the early exchanges, with Senegal dominating but failing to carve open the Qatari defence in a fairly sedate opening.
But then Boulaye Dia pounced on a horrible error from Qatar centre-back Boualem Khouki who, attempting to clear in his own box, slipped and allowed the Senegal striker to bury it from 12 yards.
Senegal doubled their lead straight after half-time, as former Bristol City striker Famara Diedhiou rose highest to power home a wonderful header.
That left Felix Sanchez's side with it all to do, their tournament hopes hanging by a thread. In fairness, they exhibited some much-improved attacking play, with Edouard Mendy saving smartly from Almoez Ali and Ismaeel Mohammad in the second half.
Ghana-born forward Muntari then wrote himself in Qatari folklore by scoring their first World Cup goal, a fine 78th minute header that might have set up a thrilling finale – had it not been for Senegal sub Dieng. He arrowed home on 84 minutes to wrap up the African side's victory.
A draw between the Netherlands and Ecuador later in the day confirmed Qatar as the earliest-ever team knocked out of the World Cup while hosting the tournament.