But the match had barely resumed before Senegal went further ahead. Diouf coolly latched onto a through ball and threaded his way through the Algerian defence, leaving the keeper no chance.
El Hadji Diouf scored a second successive World Cup hat-trick as Senegal ended Algeria's qualifying hopes with a thumping victory in Dakar.
It was Senegal's first win against Algeria after 13 previous attempts had brought only five draws and eight defeats.
"We're very happy. Now we want to go and win in Egypt and take Senegal as far as possible," Diouf said.
"We're all brothers and it shows on the pitch," he added.
Senegal continue to head Group C and their improving goal difference will be a cause of real concern to group favourites Morocco and Egypt.
Morocco also boosted their hopes of qualification with a 3-0 win against Namibia in Rabat.
Rachid Roukki was the first to score in the opening minutes of the second half and Abdeljilil Hadda added two more in the 75th and 90th minutes.
Algeria unsettled
Senegal got off to the best possible start, with Diouf slotting home a penalty in the second minute.
The penalty decision and Diouf's strike clearly unsettled the Algerians.
Djamel Belmadi tried to orchestrate attacks from out on the right flank, but Algeria lacked any co-ordination and fluency.
As against Namibia in March, Diouf and fellow strikers Henri Camara and Khalilou Fadiga created numerous chances and Algeria were lucky to go in only one down at half-time.
But the match had barely resumed before Senegal went further ahead. Diouf coolly latched onto a through ball and threaded his way through the Algerian defence, leaving the keeper no chance.
Little resistance
Beyond winning a handful of corners, Algeria offered little further resistance.
Diouf took his third in the 74th minute and Algeria left the field comprehensively beaten.
Senegal still have two tough fixtures against Morocco at home and Egypt away.
But having already got his team through to the African Cup of Nations, coach Bruno Metsu looks to be on a roll.
Algeria will have to take stock and move on. Senegal cannot wait for the next match.