Both Andean countries have 25 points, though Ecuador are in third place and Chile fourth on goal difference.
If one should lose by an ample margin on Tuesday in Santiago and fifth-ranked Uruguay (22 points) cream Argentina at the same time (2330 GMT), Chile or Ecuador could be forced into a playoff against Jordan.
"We want to qualify by beating Ecuador... that's what we're working towards," Chile's coach Jorge Sampaoli said during a press conference on Monday.
"We're seeking a victory as we always do, I can't see myself mixed up in a situation like the one you mention," Sampaoli answered, when asked about rumors the teams could pact a mutually-beneficial draw.
Chile's players, frustrated after squandering a 3-0 lead against Colombia on Friday to end up drawing 3-3, stressed they were out to win.
"We're going to give it all in those 90 minutes," defender Gary Medel said. "We're a small step from the World Cup... We won't seek a draw, or arrange anything, we're going for those three points.".
Ecuador notched a 1-0 home win over Uruguay on Friday and are looking to reach their third finals in four World Cups after missing out in 2010.
The top four teams in the South American group qualify automatically for the World Cup with Argentina and Colombia having booked their tickets. Uruguay appear resigned to facing Asia's Jordan in a two-leg playoff next month.