Qatar was pressed deep down in their own half with very few counterattack opportunities, all of which didn't post much pressure on the Senegal defense but when Akram Afif's powerful shot just outside the box went above the bar in the 15th minute.
Just one minute later, Krepin Diatta cut into the box from the left following a fast break and fired toward the near post but was denied by Qatar keeper Meshaal Barsham.
In the 34th minute, Afif squeezed into the box and fell down after clear contact with Sarr, but Spanish referee Antonio Mateu refused to give the penalty or even check the VAR.
Boulaye Dia put Senegal ahead in the 41st minute when Boualem Khoukhi failed to clear a loose ball inside the box, which bounced up nicely for Dia to fire past Barsham.
Famara Diedhiou added another for Senegal just three minutes into the second half, whose header following Ismail Jakobs' corner kick curled beyond Barsham's reach into the far top corner.
Qatar had their first shot on target at the World Cup in the 63rd minute when Almoez Ali's low strike toward the near-low corner was tipped away by Edouard Mendy.
Qatar continued their momentum and gained possession on the left shortly after, as Assim Madibo's pass found Ismail Mohamad inside the box, whose shot off his knee was tipped wide again by Mendy.
The hosts pulled one back in the 78th minute when Muntari collected a fine cross by Mohamad from the right and headed home into the far post just four minutes after he was substituted on the pitch, which marked Qatar's first-ever World Cup goal.
Qatar tried hard to level the score but things were not in their favor as Bamba Dieng made it three for Senegal in the 84th minute when he was left empty in the middle of the box to net home comfortably after a cross from Iliman Ndiaye.
With two losses in their first two games, Qatar registered the worst World Cup record as hosts after becoming the first to lose the opening game.
Qatar will face the Netherlands in their final group game on Tuesday.