The former Barnsley boss, who replaced the sacked Thomas Christiansen last week, started his tenure with a 2-1 loss at Sheffield United.
And early goals from Famara Diedhiou and Bobby Reid appeared to be condemning head coach Heckingbottom to another loss, leading to boos at half-time following a lacklustre performance.
But, like last week while winning 3-0 at home to Sunderland, City threw away another lead when Pierre-Michel Lasogga and Roofe snatched a draw in the final 18 minutes to leave Leeds eight points off sixth-placed City.
Heckingbottom received a warm reception from the crowd as he took his place in the home dugout, unaware of what was to come.
Stuart Dallas stung the palms of Frank Fielding with a shot from the edge of the box in the fifth minute, but Leeds’ defensive problems soon came to light.
United had conceded four goals in each of their last two home games and were soon 2-0 down, having failed to deal with two long throw-ins from the recalled Hordur Magnusson.
Goalkeeper Felix Wiedwald could not break through a crowd of players to punch clear and Diedhiou, with all the time in the world, coolly converted the opener from inside the penalty area in the 11th minute.
The ground was silenced again five minutes later when Reid was on hand to tap in Marlon Pack’s cross following more poor defending from a Magnusson special.
City did not look like a team out of form and, after Lasogga fired wide from distance, Ryan Kent brought a fine save out of Wiedwald.
The home fans made their feelings known at half-time and things did not instantly improve for Leeds after the break.
Diedhiou almost had a second in the 57th minute, heading a cross low towards the bottom corner which Wiedwald kept out at the second attempt.
Referee Simon Hooper then turned down Leeds’ appeals for a penalty when skipper Pablo Hernandez’s shot seemed to hit a hand of a City defender.
But Heckingbottom threw on Roofe and Hadi Sacko in an attempt to change things and Lasogga gave them hope in the 72nd minute, volleying in Hernandez’s cross at the back post.
Knowing the visitors’ shock collapse last week, Leeds sensed blood and Roofe then turned in the leveller at the back post from a corner with 10 minutes to go.
United almost won it when Lasogga headed Hernandez’s cross against the crossbar in the dying moments.