Goals from Gilbert Fiamenyo and Paul Acquah stunned the hosts who could only manage a late consolation.
The impressive win has led to beliefs that the Malian club is not as formidable a side as initially feared ahead of the return encounter in Accra.
But Kwaku Andoh wants his team to remain alert to the threat of Djoliba.
“They [Djoliba] are a good side but we were more determined for the win,” he said.
“We put in all the effort required and we are thankful it has paid off.” Hearts are now favourites to progress to the next stage of the competition as they wield a massive 2-1 advantage ahead of the return leg.