Chris Hope gave the Gills a deserved lead before the interval with a 25-yard drive that stunned Neil Sullivan as lacklustre Leeds struggled to fire.
The game flared up on the hour when Leeds defender Michael Gray and Gillingham's Darius Henderson clashed and were sent off.
Michael Flynn missed a glorious chance to seal the points before Hulse took advantage of a mix-up to snatch a draw.
Gillingham boss Stan Ternent:
"We were disappointed not to get all three points but it's a step in the right direction.
"We certainly had the best goal scoring opportunities. In some ways a point is disappointing but Leeds is not an easy place to come.
"I think if we can get to 52 points in this campaign I'll be happy."
Leeds: Sullivan, Kelly (Richardson 56), Butler, Kilgallon, Gray, Wright (King 78), Gregan, Walton, Lennon, Hulse (Deane 89), Healy.
Subs Not Used: Carlisle, Johnson.
Sent Off: Gray (61).
Booked: Gregan, Walton.
Goals: Hulse 81.
Gillingham: Banks, Nosworthy, Cox, Hope, McEveley, Southall, Smith, Flynn, Douglas, Henderson, Sidibe (Byfield 90).
Subs Not Used: Hills, Bossu, Crofts, Jarvis.
Sent Off: Henderson (60).
Booked: Douglas, Flynn.
Goals: Hope 43.
Att: 27,995
Ref: M Cowburn (Lancashire).