The team from Mendoza came from a goal down to beat River 2-1 at the Monumental, while Velez barely clung to their lead in the standings after going down 3-2 to relegation-threatened Quilmes at the Fortin.
Velez remain top with 21 points, Godoy Cruz are second on 20 and River have 19 after 11 rounds of a tight Clausura championship.
Title holders Estudiantes were also upset, 2-0 by Colon in La Plata, and are on 17 points.
At the Monumental, defender Jonatan Maidana headed River into the lead eight minutes before half-time but left-back Zelmar Garcia equalised early in the second when he beat Argentina goalkeeper Juan Pablo Carrizo with a shot from close range at the near post.
Substitute midfielder Mariano Donda stunned a crowd of more than 40,000 five minutes from time when his free-kick from 25 metres took a deflection and went just inside the stranded Carrizo's left-hand post for the winner.
"River were better than us," said Godoy Cruz's Uruguayan coach Jorge da Silva, a former River player. "We didn't have much possession and we had trouble getting the ball.
"I'm happy with the players' commitment. We played against the team with the least goals against (in the Clausura). The team showed that in difficult stadiums they have personality," he told reporters.
In fact, River have the second best defensive record having conceded six goals in the Clausura compared to only four in 10 games by Argentinos Juniors.
Velez, who went top with a 2-0 win over San Lorenzo in midweek, were level at 1-1 with Quilmes going into the final 10 minutes, but then Pablo Vazquez scored twice in three minutes for the visitors six minutes after coming on as a substitute.
Quilmes, one place off the bottom with nine points after their second successive win, had midfielder Pablo Garnier sent off for a second booking with seven minutes to go but Velez only managed to pull one goal back in added time.
Newell's Old Boys' new coach Javier Torrente made a losing debut when his side went down 1-0 at home to Banfield, who climbed to fourth with 18 points.
