Two free-kicks from captain Leonardo Valencia saw Palestino win the first leg of the Apertura final but Mauricio Prieto's 87th-minute header ensured the Wanderers will head home with some momentum ahead of Sunday's second leg.
Valencia opened the scoring in the 16th minute with a direct free-kick that clipped the top of Wanderers' wall and left visiting goalkeeper Mauricio Viana stranded as the ball looped into the net.
The home side doubled their lead just after the half-hour mark when a long ball out of defence was flicked on by Renato Ramos to Cesar Valenzuela and the 22-year-old cleverly cut inside his marker before unleashing a bullet that beat Viana at his near post.
Palestino dominated the match and deservedly made it 3-0 when Valencia struck a blistering free-kick in off the post from 30 yards with 22 minutes remaining.
But with the Wanderers set to host the return leg on Sunday, the visitors reduced their deficit with three minutes left when Prieto got on the end of a free-kick to head past Palestino keeper Dario Melo.
The Wanderers last won a Primera Division title in 2001.
