Aiming to win South America's top club title for a fourth time, Olympia were frustrated by their Colombian opponents for more than an hour before Herminio Miranda and substitute Juan Carlos Ferreyra struck for the home side.
Uruguayan Salgueiro was harshly sent off along with veteran Santa Fe midfielder Gerardo Bedoya by Brazilian referee Heber Lopes when the pair became involved in a scuffle shortly before the interval at the Defensores del Chaco.
Olimpia coach Ever Almeida sent on midfielder Alejandro Silva for the second half and the substitute was involved in both goals.
Silva was brought down by Santa Fe goalkeeper Camilo Vargas with defender Miranda converting the penalty in the 65th minute.
Ferreyra secured the victory in the 80th from Silva's fine pass that left the Argentine striker with only Vargas to beat.
Vargas made a good save to deny midfielder Matias Gimenez in the final minute while Olimpia goalkeeper Martin Silva was never troubled by Santa Fe, who are attempting to reach their first final.
The second leg is in Bogota next Tuesday.
Favourites Atletico Mineiro of Brazil are away to Newell's Old Boys of Argentina in the first leg of the other semi-final on Wednesday.