Higginbotham, who had missed the previous two matches because of a hamstring injury, scored Forest's second goal seven minutes before half-time after Garath McCleary had given Steve Cotterill's side a 25th-minute lead.
It was the on-loan defender's first goal since netting in a 4-0 victory for parent club Stoke against Newcastle at the Britannia Stadium on March 19 last year.
James Henry struck the woodwork for Millwall either side of the two Forest goals before substitute Darius Henderson pulled one back for the Lions in the 64th minute.
However, Andy Reid ended any hopes of a comeback with a fantastic long-range strike 10 minutes from time.
Millwall began brightly, perhaps buoyed by their comprehensive 3-0 win at Peterborough in midweek. Andy Keogh and Henry threatened inside the opening 15 minutes before the latter struck the woodwork.
Henry's shot was beyond Lee Camp's reach but rattled a post and then rolled to safety after hitting the Forest goalkeeper on the back.
It was against the run of play when the hosts went straight up the other end and scored.
Reid did brilliantly down the left-hand side, providing a superb cross for McCleary to head home from six yards out.
Higginbotham made it 2-0 after 38 minutes with a left-foot volley from the edge of the area after Millwall failed to clear the ball properly.
Remarkably, Henry saw another effort hit the woodwork and then rebound to safety off the body of Camp. This time the midfielder struck the crossbar with a dipping 20-yard volley.
Millwall were denied by the frame of the goal for a third time in the 64th minute when Josh Wright's shot hit a Forest defender and looped over Camp and hit the bar, but this time Henderson was on hand to head home the rebound.
The burly striker had only been on the field four minutes after replacing Harry Kane on the hour mark.
Kenny Jackett's team pushed for an equaliser but Reid ended their hopes of returning to London with a point.
The ball dropped to the midfielder 40 yards out and he advanced forwards before unleashing an unstoppable left-foot shot that flew into the top right corner of the net.