Goals either side of half time from Boulaye Dia and Famara Diedhiou put Senegal in control at the Al Thumana Stadium, only for Qatar to deservedly halve the deficit through Mohammed Muntari with 12 minutes remaining.
However, Bamba Dieng soon restored order for the Africa Cup of Nations champions, securing maximum points to keep them in contention for qualification and put their Group A rivals on the brink of elimination.
Aware of the consequences of defeat, it was perhaps understandable that the opening stages were relatively uneventful with only a long-range effort from Nampalys Mendy threatening an early goal.
Although Qatar were having their moments at the other end, a half-chance went the way of Krepin Diatta who should have done better with a header after goalkeeper Meshaal Barsham have failed to reach an outswinging corner.
The pressure continued to come from Senegal as Idrissa Gueye lashed a shot from distance marginally wide of the far post, but Qatar had reason to feel aggrieved when they did not win a penalty shortly after the half-hour mark.
Akram Afif broke clear of the Senegal backline and looked ready to end Qatar's wait for a shot on target until Ismaila Sarr clattered into the back of him, only for the referee and VAR to deny the hosts what appeared to be a clear spot kick.
Moments later, Senegal were ahead. Boualem Khoukhi failed to deal with a low ball delivered into the box and Dia was on hand to fire a shot inside the near post from 12 yards out.
Within minutes of the restart, the Lions of Teranga had their second as former Bristol City frontman Diedhiou netted a terrific header, meeting an inswinging corner at the near post to divert his effort into the far corner.
To Qatar's credit, they became the better team once they had gone two goals down, Abdelkarim Hassan sending a fizzing long-range effort agonisingly wide of the far post before Almoez Ali was denied by the outstretched hand of Edouard Mendy when his low shot on the turn was heading for the bottom corner.
Like buses, the long-awaited first shot on target was quickly followed by a second, Mendy pulling off a remarkable save from point-blank range to deny Ismaeel Mohammad.
As the game entered the closing 15 minutes, it appeared that Qatar were losing momentum, but they halved the deficit when Muntari got ahead of Kalidou Koulibaly to power a header past Mendy from close range.
However, within five minutes of Qatar possessing genuine hope of an unlikely equaliser, Senegal put the game to bed with a third goal which may prove important if goal difference comes into play upon the completion of the group.
After good work down the right, the ball was pulled back for Dieng, who was waiting by the penalty shot to clinically dispatch a first-time effort past Barsham.
Qatar continued to play for pride, far exceeding the levels of their opening-game display against Ecuador, but Senegal survived a couple of further scares to keep them in the hunt for the last 16.