Take a look back at the best of Tuesday night's match action
Jamie Paterson fired Forest into a first-half lead only for sub Williams to haul Millwall level with a goal of the highest order.
With the game heading towards extra time and a possible penalty shoot-out, Forest's Lars Veldwijk picked up a neat through ball from Oliver Burke and hit the winner in clinical fashion with a low strike beyond the reach of debut-making keeper Tom King.
The best of the night's match action is captured here in our photo gallery.