Sharp had just come on for Lewis Cook when he headed in fellow substitute Mirco Antenucci’s cross at the far post.
The game was then delayed due to a bad head injury suffered by Huddersfield’s Tommy Smith, who had tried to stop the goal.
Smith was eventually carried off to a standing ovation from both sets of fans after eight minutes of treatment in the goalmouth.
Leeds made the perfect start when Sam Byram lobbed Terriers ‘keeper Joe Murphy on seven minutes.
The visitors, seeking a first away win in 11 games, dictated play for a spell after that and could have been further ahead.
Steve Morison shot wide from a tight angle on 14 minutes from Luke Murphy’s cross from the right.
However, it was Huddersfield, seeking a fourth win in five league matches, who levelled with one of their first serious chances.
Harry Bunn headed in Jacob Butterfield’s corner from the left at the far post on 26 minutes.
Two minutes later, Rodolph Austin clattered Joel Lynch in the first of what would become a running feud between the two players.
Shortly after, Town nearly went in front when James Vaughan, playing in a mask to protect a facial injury, drew a good save from Marco Silvestri.
A Butterfield free-kick was only half cleared. Sean Scannell turned the ball back in, Bunn flicked on and Vaughan headed at goal.
On 44 minutes, Scannell held off Liam Cooper down the right channel before drilling just wide from a tight angle.
In stoppage time, Austin went in on Lynch again, with both players booked after squaring off.
Austin was then lucky not to be sent off just after the break for a third reckless lunge on Lynch.
Referee Chris Foy warned Austin and Leeds skipper Liam Cooper that the Jamaican midfielder was on thin ice.
The second half was a disjointed affair. A rare highlight was Byram’s surge into the box on 64 minutes which was ended by Mark Hudson.
Leeds players screamed for a penalty but Foy gave a corner after he ruled Hudson won the ball.
At the other end, Butterfield cut into the box from the left and fired across the face of the six-yard area on 77 minutes.
Both Scannell and Vaughan, who were unmarked, failed to connect when any touch would have seen a goal.
Leeds boss Neil Redfearn threw on strikers Antenucci and Sharp in a bid to force a winner and it paid dividends.
Antenucci missed a sitter on 87 minutes but made amends with the cross for Sharp as Leeds did the double over Town following a 3-0 win at Elland Road in September.