Millonarios, Sao Paulo in control
The return leg is Thursday at Colombia with the overall winner advancing to the final of South America's No. 2 club tournament.
The advantage with the draw probably goes to Millonarios. The Colombian capital Bogota is located at 2,650 meters (8,700 feet), a high-altitude venue that is always difficult for visiting teams.
''The draw lets us relax,'' Millonarios midfielder Mayer Candelo said.
Millonarios' defense shut down Tigre.
''The most important thing was a victory, but we couldn't get it,'' Tigre midfielder Mariano Echeverria said. ''We hardly had any chances to score.''
In Thursday's other semifinal first leg, Nicolas Castillo scored in the 69th minute to lift Universidad Catolica to a 1-1 draw against Brazilian side Sao Paulo in Santiago, Chile.
Sao Paulo took a 1-0 lead with a header from Rafael Toloi in the 21st in an evenly matched encounter at the Chilean capital.
The second leg is Wednesday at Sao Paulo.