United trailed 1-0 at the break after missing a host of chances but Sean Morrison’s dismissal turned the game on its head and the Blades scored three times before Cardiff bagged a late consolation.
“It was definitely a deserved win,” said Heckingbottom. “I was angry at half-time because we had plenty of chances to be well in front but we came unstuck from their big threat.
“To go in 1-0 down at half-time was really disappointing. But I’m pleased with how we responded, how we moved the ball and the type of goals we scored.”
Morgan Gibbs-White was the star man with a goal and two assists but Heckingbottom was keen to praise his whole team.
“Morgan was excellent,” said Heckingbottom. “We moved him infield after the sending off and played him as a No 10 with two up top to try to get him on the ball more often and it worked out well for us.
“But it wasn’t just him. The first goal was a piece of individual brilliance. The second goal he was heavily involved in but it was a fantastic team goal and the third as well.”
Mark Harris was given time and space in the area following a free-kick to fire the hosts ahead on 32 minutes.
But United took control after Morrison was sent off for denying Billy Sharp a goal-scoring opportunity seven minutes after the restart.
Gibbs-White scored a spectacular equaliser, curling his shot over Alex Smithies from 20 yards after 61 minutes, before teeing up Sharp and David McGoldrick to complete the comeback with 15 minutes remaining.
Mark McGuinness’s last-minute header proved to be only a consolation for the hosts as Heckingbottom made it two wins from two as Blades chief.
Cardiff manager Steve Morison was certain that the red card changed the outcome of the match.
“The sending off killed us but everything around that was really good, it was a positive performance,” he said.
Veteran striker Sharp could have had an early brace but the 35-year-old failed to get enough power on his header from Jayden Bogle’s cross from the right and then fired against the legs of Smithies a minute later after being put through by Gibbs-White.
The chances kept coming as Conor Hourihane curled just over from the edge of the area after Oliver Norwood picked him out from a corner, and McGoldrick shot straight at Smithies from the left of the six-yard area.
Sharp then turned provider as he crossed from the left but Gibbs-White’s stabbed effort was well wide.
Having created nothing for half-an-hour, Cardiff could have scored three in four minutes but they had to settle for one.
Wes Foderingham produced a super reflex save at point-blank range to deny Curtis Nelson, tipping the defender’s deflected header onto the post.
Cardiff broke the deadlock two minutes later. Harris controlled a delightful chipped through-ball from Joe Ralls on his chest before turning in the area and expertly firing past Fodering.
And Isaak Davies was close to doubling Cardiff’s lead but was denied by Foderingham.
The match swung seven minutes after the restart when Morrison was shown a straight red for chopping down Sharp as he raced on to McGoldrick’s through-ball.
Gibbs-White wasted the subsequent free-kick but made amends in some style with an unstoppable curling effort from 20 yards.
McGoldrick almost squeezed in a second but added the third after Sharp had struck on 73 minutes.
Cardiff City: Smithies, McGuinness, Morrison, Nelson, Ng, Ralls, Pack; Giles, Isaak Davies (Vaulks 63), Collins (Moore 63); Harris (Flint 56). Unused substitutes: Phillips, Bacuna, Colwill, Brown.
Sheffield United: Foderingham, Basham, Egan, Davies, Bogle, Norwood; Hourihane, Stevens, Gibbs-White (Osborn 87), McGoldrick; Sharp (McBurnie 80). Unused substitutes: Baldock, Berge, Mousset, Robinson, Eastwood.
Referee: J Busby (Oxfordshire).