Daniel Nardiello gave Barnsley a second-minute lead after he nutmegged Shaun Derry and beat Ehiogu before burying his finish beyond Graham Stack.
Within five minutes Leeds were level as Kandol rose unchallenged to head home.
Just after Eddie Lewis hit the post for Leeds, Nardiello scored another superb solo goal, before Ehiogu equalised for Leeds in first-half stoppage time.
Leeds boss Dennis Wise:
"It was a massive game for us. We were nervous after conceding so early but I was pleased we came back twice and we looked like the team that could win it.
"We had enough chances to win the game, good chances and it's disappointing.
"We've got some good games coming up and if they keep playing the way they've been playing they'll be fine."
Barnsley caretaker-manager Simon Davey:
"After a difficult week we would have settled for a point.
"We're disappointed we let in two headers in the box because defensively we've been magnificent recently.
"But we're very pleased with the overall performance. We could have nicked it as well as we had chances in the second half to win the game."
Leeds: Stack, Douglas, Ehiogu, Heath, Crainey, Kandol, Derry (Richardson 64), Westlake, Lewis, Blake (Healy 80), Moore (Carole 88).
Subs Not Used: Warner, Beckford.
Booked: Derry, Kandol.
Goals: Kandol 8, Ehiogu 45.
Barnsley: Colgan, Austin, Hassell, Paul Reid, Heckingbottom, Hayes, Togwell, Howard, McCann, Nardiello (Richards 79), Knight.
Subs Not Used: Letheren, Tonge, Williams, Devaney.
Booked: Hassell.
Goals: Nardiello 3, 36.
Att: 21,378.
Ref: K Wright (Cambridgeshire).