The side from the Andean province of Mendoza were joined at the top on 28 points from 14 matches by Argentinos Juniors, who beat Colon 3-1 at home for their fourth successive victory.
The two sides went a point ahead of Independiente, upset 1-0 at home on Saturday by San Lorenzo who had gone five matches without a win.
Godoy Cruz, who opened the scoring in the 12th minute with a header by defender Francisco Dutari, appeared to be cruising when Salinas and substitute Daniel Vega made it 3-0 in the opening four minutes of the second half.
However, substitute Leandro Lazzaro pulled one back in the 54th and two minutes later a controversial own goal made it 3-2.
A shot rebounded off goalkeeper Nelson Ibanez and then off defender Zelman Garcia and, although video replays showed Ibanez had scrambled back to stop the ball on the line, the goal was allowed to stand.
But Godoy Cruz left wing Cesar Carranza continued to dictate the pace and defender Leonardo Sigali made it 4-2 in the 66th minute before Salinas struck twice in the final 26 for his hat-trick.
PENALTY SAVE
Argentinos' Chilean goalkeeper saved an early penalty from Colon defender Ariel Garce before goals by Nestor Ortigoza, Jose Calderon, who looked more than a metre offside, and Ismael Sosa gave them the win.
Jonathan Bauman pulled one back in stoppage time.
Estudiantes, without suspended captain Juan Sebastian Veron but with a fine midfield performance from Jose Sosa, crushed struggling Racing Club 4-0 to join Independiente on 27 points.
Sosa scored the first with a brilliant free-kick, laid on the second for defender Clemente Rodriguez in the opening half hour and former Racing striker Leandro Gonzalez, in for the injured Mauro Boselli, added two, one in each half.
Independiente went down to their first defeat at home since inaugurating their new Libertadores de America stadium, San Lorenzo left back Nelson Benitez heading home from a corner in the ninth minute.
"When we don't have the ball we're a disaster," coach Americo Gallego said after Independiente's second successive defeat.
They had won their previous six home games and kept a clean sheet in five successive matches.
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