With Deportivo Tachira's game at Llaneros de Guanare suspended at half-time due to severe rain, Mineros could have moved into first position in the standings with a home win over recently-promoted Portuguesa but had to come from behind just to earn a 1-1 draw.
The draw saw last season's runners-up join four other clubs on four points at the top of the Primera Division with Deportivo La Guaira ahead on goals scored.
Deportivo Petare, Estudiantes de Merida and Portuguesa are the other clubs on four points.
But Mineros could have maintained a perfect start to the Apertura campaign and taken an overall lead with a victory over Portuguesa, who finished second in the Segunda Division last season to gain promotion to Venezuela's top tier.
Mineros had opened their season with a 1-0 win over the other promoted club Metropolitanos last week but fell behind after just 18 minutes at home on Sunday when Portuguesa's Jose Villafraz curled his free-kick over the wall and into the bottom corner.
Having fallen behind, the home side were forced to chase the game but struggled to get past the visiting goalkeeper, who made six saves for the match, while Portuguesa wasted a number of chances on the counter-attack.
But Mineros eventually equalised in the 75th minute when Ricardo Blanco got free at the back post to volley a cross into the net from six yards.
The hosts lost Andres Sampedro to a red card soon after but were able to hold out for a point.
Tachira (three points) sit sixth in the standings but still have to complete their second match of the season against Llaneros after the first half ended 0-0.
Caracas, Atletico Venezuela and Trujillanos also have three points with the latter having only played one game.
La Guaira lead the league after their 1-1 draw at Deportivo Lara on Saturday, with 1-1 a popular result over the weekend.
Metropolitanos versus Aragua, Estudiantes against Zamora and Tucanes' visit to Petare all finished 1-1, while Atletico Venezuela defeated Zulia 1-0.
