Uruguay have been under intense pressure and parted company with long-serving coach Oscar Tabarez after four successive defeats. However, a 1-0 win over Paraguay boosted hopes of qualification and this has been followed up with a 4-1 defeat of Venezuela.
The three points take the nation into fourth spot in the table, with both Facundo Pellistri and Edinson Cavani starting for Diego Alonso's side.
Tottenham new boy Rodrigo Bentancur got the ball rolling in the first minute before some magical wing-play from Pellistri allowed Giorgian De Arrascaeta to double the lead.
Pellistri, on loan at Alaves from the Reds, was lively but Cavani took centre stage with a well-executed bicycle kick to make it 3-0 before half-time.