Gonzalez defeated Dudi Sela 6-4, 6-4, 6-3 and put the Chileans ahead 3-1 in the best-of-five series. The decision eliminated the Israelis, who last year were surprise Davis Cup semifinalists.
Chilean Jorge Aguilar topped Harel Levy 7-6 (7-3), 6-1 after Gonzalez's win Monday, making the official final score 4-1.
Chile advances to a July quarterfinal series against the Czech Republic, which was a 4-1 winner during the weekend over Belgium in its first-round matches. The quarterfinal will be in Chile, probably on the same outdoor clay court in Coquimbo where the first round matches took place.
Gonzalez wasn't overpowering -- being called for four double faults and landing just 51 percent of his first serves -- but did manage five service breaks against Sela. He ended up winning 57 percent of the points in the match.
Gonzalez and Nicolas Massu each dropped the first sets of singles matches Saturday before recording four-set victories that put Chile up 2-0. Israel answered with a five-set doubles win Sunday by Jonathan Erlich and Andy Ram that kept the series going but Gonzalez's second singles win sealed the Chilean advance.
The Israeli-Chile series started a day late because of transportation issues caused by the earthquake that hit Chile Feb. 27.