Despite having the better of a lacklustre first half at the Reebok Stadium, Wanderers went a goal down after Jamie Paterson fired the visitors into the lead.
But Andre Moritz's free-kick found Mills, who directed the ball past Karl Darlow in the Forest goal for a 75th-minute equaliser.
The Reds, who have now gone nine games unbeaten, then almost managed to snatch it late on. Greg Halford hit the post before Andy Lonergan produced an inspirational save to keep out Andy Reid's blistering follow-up.
Bolton boss Dougie Freedman opted to continue with Jermaine Beckford and David Ngog up front after the pair both got on the scoresheet in the third round FA cup win over Blackpool.
Forest counterpart Billy Davies was missing former Aston Villa full-back Eric Lichaj, after he came off with a knock in their 5-0 thrashing of West Ham last Sunday. That meant Dan Harding came into an otherwise unchanged side.
Wanderers had the first real chance of the game when Mark Davies' shot from distance forced Darlow to make a smart low save.
Forest hit back and almost took the lead after Paterson's cross found the head of Jamaal Lascelles but from point-blank range, Lonergan scooped the ball out of the top corner to make sure the scores stayed level.
A Beckford backheel then led to Lee Chung-yong being put in on goal, but the South Korea international failed to get his shot on target.
That was Beckford's last act in the match, after the former Everton striker was taken off with a suspected knee injury. Moritz came on as his replacement just before the break.
After a disappointing first 45 minutes, Paterson got the second half off to a flyer. The winger found himself the beneficiary of a delightful through-ball from Halford and delicately slotted the ball past the onrushing Lonergan to put Forest ahead inside two minutes.
The home side went close to equalising, with Lee's cross eventually meeting the head of Mark Davies, who could only direct the ball into the side netting.
However, referee Michael Naylor brought the game back and booked Ngog for handball after his tussle for the ball with Darlow.
Despite not being fluent in attack, the Trotters managed to claim a goal which their hard work deserved.
After winning a free-kick on the edge of the box, Moritz's dangerous outswinging cross was helped on past Darlow by Mills' head.
Both sides then had late chances to win it, with Forest coming the closest late on with Halford firing against the post after a beautifully weighted pass from Henri Lansbury.
The resulting rebound then saw the ball fall to Reid, who fired towards the bottom left corner. But Lonergan somehow made sure the points were shared with a terrific one-handed stop low down.