The Brazilian side, who spent five days in the rarefied atmosphere preparing for Wednesday's match at nearly 4,000 metres on the Andean plateau, were a man short from the 21st minute.
Brazil midfielder Gilberto, formerly of Hertha Berlin and Tottenham Hotspur, was sent off for kicking an opponent off the ball.
Cruzeiro took the lead in the seventh minute when striker Wellington beat Brazilian goalkeeper Mauro Machado in the Potosi goal from left back Diego Renan's cross following a counter-attack started by Kleber.
Potosi, who hit the bar through defender Edhemir Rodriguez in the first half, equalised with two minutes remaining as the effects of the high altitude took their toll on Cruzeiro, substitute Roberto Correa scoring from Ronald Eguino's pass.
The winners of next week's second leg at the Mineirao in Belo Horizonte will go through to Group Seven which includes Colo Colo of Chile, Argentina's Velez Sarsfield and Deportivo Italia of Venezuela.
Two other preliminary round, first leg matches were played on Wednesday.
Panamanian striker Luis Tejada scored twice as Juan Aurich of Peru beat Mexico's Estudiantes 2-0 and Newell's Old Boys of Argentina were held 0-0 at home in Rosario by Emelec of Ecuador.
On Tuesday, Argentina's Colon beat Universidad Catolica 3-2 at home in Santa Fe with the Chilean side scoring two potentially decisive away goals through Juan Morales.
Venezuela's Deportivo Tachira won 1-0 at home to Libertad of Paraguay.
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
