The Liverpool striker scored twice in three minutes shortly before half-time and added two more in the second half as his side opened up a three-point lead in the qualifying table.
Uruguay dominated from the outset, with Arevalo Rios influential in midfield, but Suarez shot straight at keeper Claudio Bravo in the seventh minute with Edinson Cavani well placed and Bravo then also denied Cavani. A free-kick by Suarez hit the crossbar and Cavani shot wide before Suarez finally broke through in the 42nd minute with a left-footed finish.
The second came when Bravo gave the ball away to Cavani, whose shot was kept out on the line by Pablo Contreras but Suarez followed up to score. Chile had a goal disallowed for offside before Suarez headed in Diego Perez's cross (67) and then rounded off the win in the 73rd minute before being substituted to a standing ovation.
"It's the first time I have scored four goals in the national team, and I'm happy about that," Suarez said. "But the most important thing is that we won well. We wanted this, in front of our people and against a direct rival for qualification."
Having reached the semi-finals in the 2010 FIFA World Cup and won the Copa America in July, Uruguay are now three points clear of Argentina, who drew 1-1 with Bolivia, and Paraguay, who beat Ecuador 2-1.
Argentina even had to come from a goal down as Ezequiel Lavezzi cancelled out an opener from Bolivia's Martins Moreno, with many of the fans at the poorly attended match booing as they left the stadium.
Paraguay hit the woodwork in the first half through Marcelo Estigarribia and opened up a two-goal lead early in the second period through Cristian Riveros and Dario Veron. Ecuador's consolation came from Joao Rojas in injury time.
Colombia drew 1-1 at home against Venezuela and are level on four points with Argentina, their opponents on Tuesday, and Paraguay. Fredy Guarin put the Colombians ahead in the 11th minute, but they were unable to secure the win and Venezuela levelled in the 78th minute through Frank Feltscher.