Spaniard Juanmi Callejon pulled one back in the 89th minute for Bolivar, who were then down to 10 men after midfielder Jorge Escobar had been sent off six minutes earlier.
Bolivar, who have a record 20 titles since the Bolivian Professional Football League was created in 1977, had finished level on points with The Strongest in the final round of matches in midweek.
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(Reporting by Rex Gowar)
