After a goalless opening 45 minutes, Palestino piled on four unanswered goals, with Uruguayan striker Diego Chaves netting a brace at Estadio Santa Laura-Universidad SEK in Santiago.
Palestino are second in Group Five after five matches, level on seven points with Wanderers, who are scheduled to play leaders Boca Juniors on Thursday.
Zamora remain bottom of the group, still searching for their first point of the campaign.
Neither side could break the deadlock in the first half, but it only took Palestino one minute after half-time to hit the front courtesy of Chaves, who headed the ball over onrushing goalkeeper Edward Ibarbo.
Substitute Leonardo Valencia doubled the home side's lead in the 68th minute, dispossessing his opponent inside the penalty area and curling the ball into the corner of the net.
A swift counter-attacking move saw Chaves net his second of the match five minutes from time after Valencia squared the ball for the Uruguayan to poke into an empty net.
Mathias Vidangossy completed the scoring against the Venezuelans three minutes later with a powerful strike from long range.
Guarani were too strong for Group Eight pacesetters Racing Club on Tuesday, winning 2-0.
Second-half goals from Federico Santander and Marcelo Palau inspired the Paraguayan hosts at Estadio Defensores del Chaco.
The result reduced Racing's lead atop the table, with the Argentine outfit just a point clear of Guarani heading into the final matchday.
Elsewhere, Group One leaders Colo Colo accounted for lowly Atlas 3-1 thanks to Esteban Paredes' two-goal haul.
San Jose and Juan Aurich played out a 1-1 draw in Group Six.
