Iraq’s already slim hopes of keeping their hopes alive suffered a hammer blow a few minutes later.
Defender Rebin Sulaka had been brought into the starting lineup by Iraq coach Graham Arnold but his contribution lasted just 13 minutes.
English referee Anthony Taylor red-carded him after consulting the VAR screen for fouling Sadio Mane when the Senegal talisman was clear on goal.
It was the earliest red card of the nine so far in the World Cup, the fourth fastest in the tournament’s history.
Iraq were unable to fashion a chance in the rest of the half and despite their one-man advantage Senegal could only muster one, Ismail Jacobs’ fierce strike from outside the box just going wide with the keeper beaten.
Senegal came out for the second half bristling with intent.
Iraq had been further destabilised as they had to replace goalkeeper Ahmed Basil, who had taken a knock in the first half, with Jalal Hassan at the break.
Hassan survived the early wave of attacks but was helpless when Senegal finally got into their stride.
Ismaila Sarr tapped in in the 56th minute, for his third goal of the tournament, after a dreadful error by former Manchester United player Zidane Iqbal deep inside his own half gifted Senegal possession.
The relief of the second goal had Sarr lying prone on his back pumping his fists with joy.
Then came the Gueye show and it had the fans off their seats.
Within 89 seconds of coming on as a substitute he let rip from outside the box with a sublime curling effort that gave Hassan no chance for 3-0 in the 59th minute.
The Villarreal midfielder possibly outdid that effort with a vicious half volley 12 minutes later that flew past the keeper.
Arnold was reduced to leaning on the dugout and ruefully shaking his head, and could only watch as Iliman Ndiaye scored with another screamer eight minutes from time.
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