Flying winger Patrick Razak put Hearts in the lead in the 9th minute of action, drilling home after latching on a cute chipped pass from Thomas Abbey.
But the hosts hit back two minutes after the break through Nicholas Gyan, who headed home after the Phobians had failed to clear from a setpiece.
Hearts were denied a certain winner by the match officials when Ivorian striker - and substitute - Alexandre Kouami fired home expertly past goalkeeper Andoh in the 90th minute only to be flagged offside.
Head Coach Frank Nuttall made two changes to the side that drew with Medeama in the last game. Samuel Yeboah was handed his first start of the campaign, in place of Samudeen Ibrahim who dropped to the bench, whilst captain-on-the-day Thomas Abbey replaced the convalescing Isaac Mensah in the team.
The hosts were very impressive in the opening minutes of the game but it was the Phobians who looked more threatening.
Razak missed a golden opportunity to put Hearts in the lead in the third minute of the game, fluffing a lay off from Cosmos Dauda in the six-yard box much to the thankful surprise of Dwarfs.
However, the winger made amends for his miss, drilling home beautifully after chasing a cross from Abbey. It was a difficult chance to score but Razak once he had paced past his man cut back inside to completely beat his marker before slotting past the hapless Frank Andoh.
The home side took over the control of the game and they were very promising on their attacks. On many occasions, they were denied by the very impressive Benjamin Mensah who went home with a deserved MOTM award.
In the 27th minute, Hearts could have been awarded a penalty when Dwarfs stopped Andoh struck out an arm to push captain Abbey down in the box but the referee allowed play to continue despite the stadium falling into a guilty silence.
Dwarfs winger Alhaji Mustapha failed to capitalise two minutes later, blazing over after the ball had fallen kindly into his path from a corner kick.
The hosts missed a similar chance just on the stroke of halftime with Osman Mohammed blasting across the face of goal after being found unmarked in the box.
After the break, Dwarfs Brazilian coach brought on Eric Bosomtwe as the hosts took the game to the Phobians. Two corner kicks in quick succession served notice of their intent for the equaliser.
And they got it in the 47th minute. Hearts failed to properly deal with the cross into the box, for Gyan, who appeared a yard offside, to head home.
Buoyed by the leveler, Dwarfs laid siege in the Hearts box and kept probing and probing only to be constantly denied by the imperious Ben Mensah.
However, Hearts soon stymied the pressure and started asking questions at the other end. Malik Akowuah's long range drive was blocked for the strikers to fight for the rebound in the box. This came about after a well worked routine from a corner kick.
A few minutes later, Kodie's persistence helped him to recover the ball inside the box but his low shot was coolly saved by Andoh. The former Liberty midfielder was back in the thick of affairs shortly afterward but his volleyed effort from the edge of the box was deflected out for a corner kick.
Hearts look the more certain to score as the minutes wore on with the introduction of Kouami but when he went through on goal after beating his marker for pace. He was still not flagged but allowed to continue racing with the ball for more than 15 meters. One on one with the keeper, the Ivorian drilled home unawares of a late flag strangely lifted by Assistant 1 Joseph Sey.
The decision was very hard to fathom for the Phobians who still await a first win of the campaign.
HeartsXI vs Dwarfs: Benjamin Mensah, Anthony Nimo, Joshua Otoo, Inusah Musah, Vincent Atinga, Malik Akowuah, Patrick Razak (89 Fatawu Mohammed), Daniel Kodie, Cosmos Dauda (72 Alexandre Kouami), Samuel Yeboah, Thomas Abbey (c)
Booked: Malik Akowuah (38), Anthony Nimo (64), Daniel Kodie (81).
Unused substitutes: Samuel Akurugu, Robert Addo, Samudeen Ibrahim, Amin Alhassan, Bright Lukman.
Dwarfs XI vs Hearts: Frank Andoh, Christopher Bonney, Ebenezer Ackon, Mohammed Musa, Awudu Masawudu, Nicholas Gyan, Alhaji Sohabi (45 Eric Bosomtwe), Solomon Gyasi (70 Justice Mensah), Osman Mohammed, Mustapha Alhaji (80 Albert Hammond).
Booked: Alhaji Mustapha (34)
Unused substitutes: Denis Korsah, Francis Mensah
MAN-OF-THE-MATCH: Benjamin Mensah
Report By: Anwar U.Larry