Captain Liam Cooper headed the only goal of the game in the 31st minute to give Heckingbottom his first win since taking charge at Elland Road.
Brentford did have their chances to take something from the game, with Felix Wiedwald pulling off a brilliant first-half save to keep out John Egan’s volley.
Florian Jozefzoon, Ollie Watkins and Kamohelo Mokotjo also wasting good chances for the Londoners.
But the win could have been more comfortable for the home side too, with Daniel Bentley saving brilliantly to keep out Pierre-Michel Lasogga in an entertaining first half.
‘It’s good to have the first win, it is a reward for the hard work of the players and reward for everyone,’ said Heckingbottom.
‘Brentford are a good side and it is excellent to keep the clean sheet.
‘There are lots of positives to take from the performance. Lots of organisations goes into it and to be successful in this league you have to be able to defend and stop teams as well as hurt teams.
‘Brentford are great team at creating chances when it goes end to end
‘We could have been better at times with the ball, we gave it away too easy at times and could have shown more composure.
‘We grew as the game went on and deserve that victory
‘We stepped up a bit more in the second half and kept them away from our box a bit more.
‘We had chances to get the second and close the game out and that is an area where we will need to be better.’
Brentford boss Dean Smith felt his side did not do enough to win the match.
‘They started the game quite well in the opening minutes, but then we were in control. I don’t think they saw the ball,’ he said.
‘It looked like it was going to be one way traffic, but then the Leeds goal comes from an offside position.
‘At half-time we were still in the game and we felt we had a chance in the second half.
‘We were too sloppy on the ball and the subs didn’t work today. We were very poor on the ball, certainly in the second half.
‘We can take the positives from a six-point week. We’ve lost a game from a linesman’s decision.
‘We didn’t do enough to win the game. They left the grass longer to make it a slow game.
‘We should have had a penalty when Neal Maupay gets thrown to the ground. You want the big decisions to go your way, but they didn’t today.’
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