Fletcher netted with a diving header in the 22nd minute after he met a Colin Nish pass across goal.
Earlier, Colin Nish had hit the Accies' crossbar with a strong header.
Sheridan grabbed a second after Hibs' Colin Nish had been sent off and Craig's penalty rounded off an impressive night for the hosts.
Hibs were without Sol Bamba and Colin Nish through injury, with youngsters David Wotherspoon and Paul Hanlon both coming into the starting line-up.
Colin Nish fired a tame effort at Zaluska as the hour mark approached, then Fortune warmed the hands of Stack at the other end.
Experienced campaigners like Kevin McBride, John Rankin and Merouane Zemmama were posted missing in midfield, while Colin Nish laboured forlornly in the lone striker's role.
"Colin Nish was a name that was put to me straightaway when I came in but I couldn't decide because I hadn't seen the player, " said Paatelainen.
But he was forced to bring Steven Thicot into defence in place of the injured Michael Hart, while Colin Nish started in place of the suspended Kevin McBride.
However, it was the visitors who scored again after 55 minutes, when Colin Nish's shot across the face of goal was turned home by Stokes for his second of the match.
Hibernian manager Colin Calderwood made a double substitution in an attempt to change the pattern of play with Ian Murray and Colin Nish withdrawn and David Wotherspoon and David Stephens sent on.
Hibs made an encouraging start to the game and could have opened the scoring in the third minute after Dean Shiels fed Colin Nish inside the box, but his pass to Fletcher fizzled out.
Hearts looked to be dead and buried when Balogh was sent off for chopping down Fletcher after the striker was sent clear through the middle by Colin Nish on the stroke of half time.
Colin Nish nodded wide from a David Wotherspoon cross, but Ma-Kalambay was then called back into action when Invincibile reacted to try a shot at the right-hand post that the Hibs goalkeeper blocked with his legs.
However, Hibs were back on level terms within five minutes of the hosts' opener when Stokes ran onto a Colin Nish ball down the right and drilled home a low effort into the bottom corner of Brown's net.
John Rankin, Colin Nish and Dean Shiels had paid for last weekend's defeat at home to Kilmarnock by being dropped to Hibs' bench, while captain Rob Jones was missing through injury as Derek Riordan, Lewis Stevenson and Steven Thicot were recalled.
Killie, who finished second bottom of the Scottish Premier League last term, also lost Steven Naismith and Colin Nish during the course of last season and have so far only been able to bring in one new striker in the shape of Allan Russell from Airdrie United.
应用推荐