The hosts were trailing by two goals midway through the second half, but substitute Kazenga LuaLua halved the deficit and David Lopez dragged them level with three minutes remaining.
New Zealand international Wood is expected to leave parent club West Brom in the new year and Seagulls boss Poyet admits he is interested in bringing him back to the south coast, where he had a successful spell on loan a couple of seasons ago.
But Lions manager Kenny Jackett is ready to splash £1million to make Wood's current loan deal a permanent switch to south London.
And the 21-year-old illustrated why he has become such hot property with an instinctive first-half finish and a cracker after the break.
The visitors had been dealt a blow before kick-off when Wood's strike partner Andy Keogh broke his toe in the warm-up.
Liam Trotter was pushed further up front as Jackett reshuffled his line-up, and the midfielder could have opened the scoring in the first minute with a free header but his effort went straight at Tomasz Kuszczak.
Will Buckley headed a corner from Lopez wide in Brighton's first attack, but it was Millwall who struck first in the 26th minute.
Shane Lowry crossed from the left and Wood darted in at the near post to get the slightest touch and divert the ball into Kuszczak's net.
Brighton almost hit straight back from a Lopez free-kick but skipper Gordon Greer's looping header came back off the crossbar.
However, Poyet had seen enough and made a change with seven minutes of the first half still to go, hauling off defender Lewis Dunk in favour of winger LuaLua.
Brighton improved after the interval and they were denied by the woodwork again in the 54th minute when a free-kick from Lopez crashed against the post.
But barely a minute later Wood doubled Millwall's advantage in stunning style, cutting across the penalty area and curling in a superb shot past Kuszczak and into the top corner.
Yet Brighton pulled one back in the 61st minute when LuaLua turned inside and thumped a fierce drive through a crowd of players and past Lions keeper David Forde.
The Seagulls thought they had levelled when Adam El-Abd prodded the ball goalwards from a yard out but Lowry somehow hacked the ball off the goal-line.
However, they did grab a point with two minutes to go after Craig Mackail-Smith was felled by Mark Beevers and Lopez stepped up to tuck in a dramatic leveller.