The Enterprise is between missions and is struck by a quantum filament, trapping everyone more or less where they are, killing intraship communications, and knocking out primary life support and the warp engines. Picard, trapped in a turbolift with three elementary school children, is injured when the lift first falls. Meanwhile, on the bridge, the three relevant characters are O'Brien, Ensign Ro, and Troi, who as the senior officer is placed in command. In Ten-Forward, Worf is left to take care of the wounded (and a very pregnant Keiko O'Brien) while Riker and Data head through a crawlway to try to get to Engineering. Finally, Bev and Geordi are trapped in a shuttle bay-and a plasma fire is spewing radiation into the bay, threatening both the people and some canisters of chemicals, which are likely to explode.

Riker and Data end up with their retreat cut off by a coolant leak and their advance stopped by a huge current arc. Data volunteers to use his (non-conducting) body to block the circuit, claiming that his head will survive and can be detached for use in Engineering. Riker, having no other options, approves. While Picard tries to get the children working together to get them all out of the lift, Ro manages to power up the Engineering console and finds that the warp containment field is slowly failing, which will eventually lead to the entire ship exploding.

Once the lift's hatch is open (and the children refuse to leave the injured Picard behind), the group begins working on ways to leave and climb up to an open deck. Meanwhile, Bev and Geordi decide the only way to both keep the chemicals safe and put out the plasma fire is to depressurize the shuttle bay. And, as if things weren't bad enough, Keiko suddenly goes into labor.

While Troi decides not to follow Ro's advice (namely, to separate the saucer and get the hell away from the warp engines, assuming there's no one left alive in the drive section) and sends enough power down to Engineering so that anyone there can at least realize there's a problem, Picard and the children leave the lift (just in time, as its emergency clamps fail and it falls) and begin climbing to a door that will open. Bev and Geordi depressurize the bay, putting out the fire, and Bev manages to repressurize it just in time.

Riker and Data's head reach Engineering and manage to restore the containment field just before it collapses, Picard and the kids make it to an open deck, and a very inexperienced Worf manages to successfully deliver Keiko's daughter. Later, once everything is running smoothly again, the children give Picard a commemorative plaque to thank him for all his help.