Spanish veteran Pablo Hernandez slotted the ball into an empty net after Henderson had passed the ball to Leeds youngster Jack Clarke, to send Leeds to the top of the table.
The visitors -- who could be overhauled by Norwich if the 'Canaries' beat Rotherham later on Saturday -- held on for their third successive win despite some nervy moments especially when Conor Washington's acrobatic overhead kick rattled the crossbar.
“That was a massive win. It was a difficult game, but it’s important to stay in this position", Hernandez told 'Sky Sports'.
"The next month is very important with so many games.”
Sheffield United started the brighter and David McGoldrick went close after 10 minutes bringing a fabulous save from Leeds Northern Ireland international Bailey Peacock-Farrell.
The visitors suffered a major injury blow 10 minutes later when captain Liam Cooper hobbled off to be replaced by Finnish Under-21 international Aapo Halme.
McGoldrick was avery fortunate to escape without even a yellow card for a studs up foul on Polish international Mateusz Klich.
The previously impeccable Henderson gifted Leeds a goal with eight minutes remaining. Desperately trying to save a poor back pass by John Egan from going for a corner, he passed it straight to Clarke.
The 18-year-old forward kept his head and laid it across the area to Hernandez who made no mistake.