The hosts were ahead after just five minutes, when John Rankin timed his run into the box perfectly and headed the ball into the back of the net.
The away side continued to pepper Cierzniak's goal with shots from all angles, and five minutes before the break they could have been ahead when Griffiths found space in the box, but the striker's shot bounced clear off the post.
He made up for it shortly after half time, after being put through by Matt Done, Griffiths opened up his body and curled the ball into the top corner from 25 yards out.
Hibernian continued to win free kicks around the penalty area, but United defended well and kept the score within one.
They were rewarded for their efforts five minutes from time. A poor challenge from Ryan McGivern brought down Gary Mackay-Steven inside the penalty area, giving the referee no option but to award the penalty. Top scorer Johnny Russell made no mistake from the spot and Dundee United were level.
Both teams tried to push for a late winner, but to no avail. Hibernian move up one place to sixth, while Dundee United remain in ninth.