The visitors started the game brightly with a number of slick passing moves, before Marvin Emnes broke free inside the box, only to see the Millwall defence scramble back to crowd the ball out of play.
Emnes looked impressive early on and was in the thick of things again having been been found by Curtis Main, but once more he was crowded as he looked for a sight on goal.
Both sides found it hard to control the ball given the slippery conditions on show, but Liam Feeney did well to break away on the counter, only to deliver a fairly tame across into the box, which was cleared easily by the Boro defence.
The second half was only four minutes old when Emanuele Ledesema put Boro 1-0 up with a left-footed shot from outside the box.
As the match entered the final 10 minutes, both sides stepped up their search for a goal. Curtis Main had a shot blocked for the visitors, while Liam Trotter fired over when well placed.
However, Adomah did manage to find the net when he latched onto Ledesma's through-ball and slotted home past Forde.