Dexter Blackstock, signed on loan from Nottingham Forest this week, headed home a 73rd-minute equaliser with his first touch less than 60 seconds after stepping off the bench to draw the visitors level.
But four minutes later Stead rifled home an angled shot into the bottom corner to seal Huddersfield's first win in six league matches.
The goal was his first since returning to the Terriers for a second spell after his contract at Bristol City had expired in the summer.
Huddersfield winger Danny Ward smashed home a first-half equaliser after Leeds striker Matt Smith had given the visitors an early lead and Blackstock struck with a fine header after Tom Lees' own goal had edged the home side ahead in the 62nd minute.
Leeds raced ahead in the second minute when Smith brushed aside marker Joel Lynch at the far post to head home Alex Mowatt's corner.
It was Smith's third goal in two matches and his fifth of the season following his summer arrival from Oldham.
But the visitors' lead lasted barely eight minutes as Huddersfield equalised following their first corner.
Adam Hammill delivered the perfect ball to Ward on the edge of the penalty area and the winger took one touch before slamming home an unstoppable left-footed shot beyond Leeds goalkeeper Paddy Kenny.
Huddersfield grew in stature as the first half progressed, with Hammill going closest after teasing Warnock on the edge of the area and curling a super effort that Kenny did well to tip over the crossbar.
Ward pulled a right-footed shot wide after swivelling into space inside the area, but that was the last of the goalmouth action before half-time.
Huddersfield replaced teenage midfielder Duane Holmes, who had made his first start for the club, with Sean Scannell during the break and were first to threaten at the start of the second period.
Right-back Jazz Richards' deep cross was headed wide before Smith robbed Paul Dixon at the other end and fired a low shot off target.
Leeds missed a golden chance to regain the lead on the hour when a brilliant interchange between Byram and Austin set the visitors' captain free, but his cross to the far post was skewed wide by Murphy from six yards.
Leeds were made to pay soon after when another curling cross from Hammill skimmed off Lees' head and bounced inside Kenny's left-hand post.
Stead then hit the outside of the post after he had rounded Kenny in a one-on-one as the home side threatened to run away with the game.
But the introduction of Blackstock for Murphy in the 72nd minute proved inspirational.
Mowatt swung over a free-kick from the touchline and Blackstock rose unmarked to head home with his first touch less than 60 seconds later.
However, Huddersfield were not finished. Hammill cut the ball back to the edge of the area after being played in down the right by Scannell and Stead turned sharply to arrow his shot into the bottom corner.
Smith was guilty of a glaring miss at the far post in the 87th minute and referee Neil Swarbrick was unmoved when Austin was bundled over in the area in the closing stages.