I think this was Law & Order: SVU, but can't be sure. Basically the plot was (I think) a killer who had a girl trapped in a house, but the police didn't know the location. They had him in an interrogation room, and secretly kept moving the time forward little by little. After his deadline passed (he thought), they were able to save the girl in time. Does this ring any bells at all?

They did something like that a few seasons ago on Criminal Minds, except they did it to a terrorist and they moved the time ahead to thwart the planned attack.

was also an episode of Third Watch where somebody was having their blood drained slowly.

I don't think it was either of those shows.

Yes, Chris Elliott was the killer in that episode. They fooled him into believing it was later than it was.