The former Manchester United midfielder's stunning ninth-minute overhead kick did the damage as the Lions triumphed at The Den.
It was only Tunnicliffe's second goal of the season and first for 13 games as Neil Harris' side claimed a second home league win on the bounce to make it a happy festive period.
Forest had chances to at least snatch a share of the points, but the battling Lions deserved their victory as they look to continue climbing away from the wrong end of the table.
Harris named an unchanged side from the team which beat Reading on Boxing Day.
And his players rewarded him within the first 10 minutes when Tunnicliffe gave the home side the perfect platform to beat opponents who sat 10 places above them in the Championship standings before kick-off.
Forest failed to deal with Ryan Leonard's corner and Tunnicliffe timed his overhead effort to perfection for a fine start.
Keeper Jordan Archer produced a smart save from Joe Lolley's goalbound strike to prevent Forest getting on level terms in the 27th minute.
Midfielder Matthew Cash tried his luck from distance at the other end, but his effort flew agonisingly wide of the target.
Cash had another good chance six minutes after the restart, but his rasping drive was also wayward.
Jed Wallace went close to doubling the hosts' lead shortly after the hour mark but his shot was deflected on to the roof of the net.
Forest boss Aitor Karanka threw caution to the wind with a double substitution in the 65th minute as he looked to get his side back on track.
But even the introduction of leading scorer Lewis Grabban – who has bagged 14 goals this term – and Saidy Janko could not provide the answer the visitors were looking for as Millwall defended solidly.
Striker Steve Morison did well to meet Shane Ferguson's whipped in corner, but his header was over the crossbar as the Lions looked to finish the job with 15 minutes remaining.
Morison should have put the contest out of reach in the final minute of the game after some excellent work from Aiden O'Brien. His inch-perfect pass just needed Morison to pick his spot, but his shot cannoned off the far post.