Barnsley started the brighter of the two teams but were soon pegged back by Chris Wood’s opener in the 18th minute. The prolific striker netted his 15th of the season with a near-post flick from Pablo Hernandez’s corner.
The home side were level going into the break as Tom Bradshaw headed Adam Armstrong’s cross into the far corner of the net in the 45th minute.
And just three minutes into the second half, Ryan Kent put Barnsley into the lead. The Liverpool loanee received the ball with his back to goal before turning and powering a left-footed shot past Rob Green
Conor Hourihane added a third in the 54th minute with a neatly placed free-kick into the top left corner of Green’s goal.
Wood gave Leeds a route back into the game after 68 minutes, slotting home a penalty after Marc Roberts was adjudged to have handled inside the box.
Heckingbottom said: “I was pleased from the first minute to the last. We did everything we spoke about before the game.
“If I’m honest I think the only thing that concerned me about Leeds today was them on the counter and their set plays.
“I think we deserved the win and to come back from behind shows our character.
“We demand a lot and the players love it. They love performing that way and it’s good to watch, high intensity and high energy.
“When we play as well as that it’ll be tough for a team to beat us.
“We’ve got good players who are good on the ball and that’s what won us the game.
“Conor Hourihane is a Barnsley player and until a bid gets accepted that’s what he’ll continue to do.
“All we can do is worry about how we want to play and go out there and execute it.”
Leeds boss Garry Monk said: “A disappointing result and we’re frustrated to lose the game.
“We were slightly off defensively, particularly in the second half.
“We knew they would come out of the blocks, I thought they started well.
“We got through that period, got the goal and started to have more control of the game at that point.
“We didn’t get that second goal which we should have done; I felt there was a clear penalty on Bartley.
“We made the critical mistake of conceding on the stroke of half-time. We were too reactive and they got the goal.
“In the second half they get two quick goals and from our point of view they’re poor goals to concede.
“We’ve been playing at such a high standard so we will have this odd game now and then where we don’t perform at our usual high levels.”