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.
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.
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.
