Millwall had taken the lead through Henderson, who fired home from outside the area after 15 minutes.
Owen Coyle's side struggled to create chances in the opening half, and trailed going into the break.
The Trotters had a golden opportunity to go in front on the hour, when Bolton were awarded a penalty after the winger was fouled by Nadjim Abdou.
Eagles took the spot kick himself, but he missed the target and Millwall held out to claim a share of the points.
Henderson scored a dramatic winner in the 90th minute with a superb solo effort, sidestepping two players before launching a drive into the bottom right-hand corner of the net.
Millwall's first win in five lifts them above the relegation places, level on 11 points with Bolton, who have now only won once in their last 50 away games.