The continental club masters made it to the penultimate qualifying round after a solid come from behind to win against Senegalese side Olympique de Ngor.
Goals from Eric Kumi, Robin Gnagne and Paul Acquah stole victory for the Phobains with the Senegalese side also getting two of their own.
Goalkeeper Soulama who is proving to be a bargain again had to pull off saves to ensure Hearts were solid at the back, but says the collective team effort sent them through.
“We played well with a strong determination that most people do not credit us with,” Soulama told GHANAsoccernet.com
“I did my job, but the entire team played well and that has been the secret.
“I think our performance is a strong statement of our team unity.”
Hearts will now take on Malian side Djaliba in the next round of qualifiers.