The Phobians took a giant step towards reaching the final stage with the vital away win.
After a goalless first half, Hearts turned on the style by snatching the opener on 54 minute through leading scorer Gilbert Fiamenyo.
The burly striker walked the ball into a yawning after the Djoliba goalkeeper clashed with his defender.
Youngster Paul Acquah doubled the lead in the 63rd minute when he flicked the ball over an on-rushing defender before firing past the goalkeeper.
But Hearts were reduced to ten men when captain Robin Gnagne picked up his second yellow card for a high foot challenge.
Two minutes later, Djoliba reduced the deficit from the spot when goalkeeper Abdoualye Soulama felled a player inside the box.
The return leg will be played at the Accra Sports Stadium on 03 May.
Meanwhile, coach Herbert Addo has attributed his side’s impressive run in the Confederation Cup to the dollar winning bonuses paid to his players.
The Phobians took a giant step towards reaching the final qualifying round after the 2-1 win over AC Djoliba in Bamako .
The return leg is in a fortnight at the Accra Sports Stadium .
“If you are working with people who are not determined and not prepared to win, then you are wasting your time,” Addo said.
“But my boys have tasted victory and about five of them had never sat in planes before but they have tasted the air, enjoyed it; and tasted a few dollars and have enjoyed it more.
“So they want more dollars, more air and more playing time. I think they are determined and I wish the supporters could follow us everywhere we go, not only during home matches.
“The boys have got a lot of confidence and we are going all out in the rest of the matches left in the competition.”
In a related development, in-form Hearts striker Gilbert Fiamenyo has insisted progress to the next stage of the CAF Confederation tie between Malian giants AC Djoliba and the Phobians will go down to the second-leg in Accra.
The Phobians playing with ten men, stunned Djoliba at the Stade 26 Mars in Bamako, beating them 2-1 with striker Fiamenyo opening the scoring before Paul Acquah sealed the points from the first-leg.
“We came here to win and definitely we have won. We are happy and we thank God and the fans and everybody who supported us but the second-leg is in Accra where we will finish up things,” he said.
Meanwhile, each member of the Accra Hearts of Oak playing body that made the trip to Bamako will pocket an amount of $700 as reward package for beating Djoliba AC on Friday evening.
The Phobians took a giant step towards sealing qualification into the next stage of the CAF Confederations Cup competition as they beat Malian side Djoliba AC 1- 2 in the first-leg tie at the Stade Moibo Keita in Bamako.
And in reward, board chairman Togbui Afede XI and management of the club have rewarded the players with US$700 each, with $200 as being their per diems.