Brighton rarely threatened on a difficult, bobbly pitch, although veteran striker Nicky Forster almost hit back immediately after Morison's goal but fired narrowly over.
Seagulls defender Tommy Elphick had a header cleared off the line late on and Glenn Murray also saw an effort rebound off a post.
Millwall striker Shaun Batt was twice denied by Kuipers as the Lions threatened on the counter-attack.
Kuipers saved an early shot from Chris Hackett before Elliott Bennett put a powerful free-kick just wide for Brighton. Brighton skipper Andrew Crofts went close with a fierce 20-yard drive which flew just over the crossbar in the 25th minute.
Source: Team Talk