After two straight draws in the league, the Phobians bounced back in the cup competition as Joseph Esso's penalty ensured a 1-0 triumph over the Division One club in the round of 64.
Henry Wellington's outfit, who face Inter Allies in the topflight on Thursday, are on course to make the final of the FA Cup as they did last season.
"We used our experience to beat them [Wise] and I can say we are happy to qualify to the next stage of the competition," Cobbinah said.
"This season has been full of ups and downs for us.
"We were motivated enough for the game and this win could serve as a morale booster ahead of the game against Inter Allies on Thursday.
"Little by little, we will pick up."
Hearts sit 10th on the league table after 12 matches.
Their last two league games ended goalless with Liberty Professionals and Wafa.
Allies, meanwhile, hold the fifth position on the log.