Watford had started well and Bruce Dyer gave them the lead after 10 minutes, slotting home Heidar Helguson's cross.
Veteran striker Brian Deane's header caused panic in the Watford penalty box and Jermaine Wright drilled the ball home for Leeds' equaliser.
Dyer restored Watford's lead after intercepting Sean Gregan's poor backpass before Clarke's late goal.
Watford boss Ray Lewington
"Yes we are disappointed, but it says a lot that we can come to Elland Road and be disappointed with a point.
"I thought particularly in the first half, we were good. We were very good and we carved out some really good
opportunities.
"I think we saw the finishing line and stopped doing the things we had been doing for the previous 80 minutes. But I can't complain - I thought that we worked really hard and were a little bit unfortunate."
Leeds: Sullivan, Kelly, Carlisle, Butler, Pugh, Wright, Gregan,
Walton, Healy, Deane (Joachim 45), Oster.
Subs Not Used: Carson, Spring, Lennon, Kilgallon.
Booked: Walton.
Goals: Wright 21, Carlisle 86.
Watford: Lee, Smith, Cox, Dyche, Darlington, Chambers, Gunnarsson, Mahon, Ardley (Young 90), Dyer (Fitzgerald 87), Helguson.
Subs Not Used: Chamberlain, Gayle, Demerit.
Booked: Helguson, Smith.
Goals: Dyer 9, 71.
Att: 24,585
Ref: M Jones (Cheshire).