Hulse struck his fourth goal in as many games since signing on loan from West brom and handed Kevin Blackwell's side a deserved point from this hard fought tussle.
Both sides started the game desperate for a win that would move them within a point of sixth-placed Reading.
It took Millwall just 17 minutes to break a run of one goal in five games when defender Paul Robinson tapped home his first strike since returning from a loan at Torquay.
It was no more than the Lions deserved after a bright start, just two minutes in Josh Simpson should have done better than head Peter Sweeney's cross right into the hands of Neil Sullivan and Danny Dichio was just inches away from converting Tony Craig's cross.
At the other end Darren Ward almost diverted Aaron Lennon's centre into his own net before Michael Gray bent a 25-yard free-kick inches wide.
Lions winger Simpson then cut in off the left and fed Sweeney whose well struck drive was pushed wide by Sullivan.
Sweeney swung a corner to the back post where an unmarked Craig drove a cross goal for Robinson to tap home five yards out.
Lennon's direct running was causing problems for Millwall and Marvin Elliott was booked for hauling him down.
Leeds started the second half brightly and Gary Kelly tested Andy Marshall's reflexes with a stinging 25-yard drive.
Simpson then headed inches wide from six yards after Dichio flicked on Robinson's deep cross.
The home fans appealed in vain for a penalty when Sweeney was sandwiched between two Leeds defenders but referee Barry Knight was unmoved.
Moments later Dichio drove wide from the edge of the area, but Leeds hit back with 13 minutes to go.
Hulse brought down a long ball from Kelly, turned on to his left foot and buried the ball into Marshall's bottom right-hand corner.
Sean Gregan and Shaun Derry were both booked for fouls in midfield as the battle heated up late on, but a point apiece was about right and keeps both clubs' play-off hopes alive.