The hosts have not suffered a defeat in their last 12 games as they continued their reign in South America by seeing of their guests in Montevideo
The Liverpool star scored four goals, two in the span of three minutes late in the first half, as Oscar Tabarez's men remain atop the table in Conmebol qualifying with seven points.
On Wednesday, Chile coach Claudio Borghi suspended Arturo Vidal, Jorge Valdivia, Jean Beausejour, Gonzalo Jara and Carlos Carmona for missing curfew, but the help the players would have provided had they played may have not made a difference in an stunning display by Suarez.
With Alexis Sanchez on the bench to start the game, Chile suffered dearly as the home side terrorized their defence every couple of minutes.
Suarez should have put the hosts up eight minutes in with a lovely run on the right side of the box, but his no-look touch towards the front post was saved well by Claudio Bravo, who denied Edinson Cavani from close minutes later.
More chances came for the two-time World Cup winners as Suarez ticked a ball off the post from inside the box, only to hit the cross from a free-kick from around 30 metres just three minutes later.
The fans were finally awarded a goal as Suarez, after several close calls, punished Borghi's men with a stunning strike minutes before the break. From 25 metres out, off a pass from Arevalo Rios near midfield, the former Nacional man drilled a perfect, low shot into the right corner of the goal for the slim advantage.
Two minutes later, Suarez doubled the score after Bravo fumbled the ball at the top of the box, resulting in a lobbed shot from Cavani that was cleared off the line by Pablo Contreras. Suarez jumped into the air in front of goal to fight for the 50-50 ball with Waldo Ponce, but the strength of the Uruguayan sent the ball off his shoulder and into the right side of the net.
Chile's night was worsened in the second half when Suarez again found the net, heading home a cross from Martin Caceres with just over 20 minutes to go.
Then, just six minutes later, Suarez volleyed home another goal from the top of the box into the right corner to cap off his best performance with the national shirt.
With the win, Uruguay remain undefeated in qualifying over three games and will play Italy on Tuesday in a friendly. Chile, who have three points from three matches, will be back in action on Tuesday against Paraguay.