Lions forward Keogh chipped his spot-kick down the middle of the goal after being brought down by Zat Knight in the ninth minute.
But fellow Republic of Ireland international Andrews ensured it was all square at the interval when former Wanderers defender Danny Shittu fouled Lee Chung-Yong.
Some slack defensive play from Wanderers gifted Millwall an early lead. Tim Ream's pass into midfield sold Andrews short and Liam Trotter stole in to release Keogh. The former Wolves striker had his heels clipped by Knight and picked himself up to cheekily beat Adam Bogdan.
Lee bustled forward in an attempt to engineer a Bolton response and teed up David Ngog, but the ex-Liverpool man's effort was scuffed into the arms of Millwall goalkeeper David Forde.
Kenny Jackett's men looked to re-assert themselves and Bogdan was not breathing easily when Liam Trotter and James Henry produced superb efforts from distance that were narrowly off target.
Wanderers were level 11 minutes before the break after a deft Kevin Davies pass sent Lee into the area and Shittu clumsily intervened. Andrews opted for a more conventional method than Keogh, striking the spot-kick low into the bottom left corner with Forde guessing wrong
Forde produced the save of the match in the 83rd minute, turning Marcos Alonso's 25-yard drive behind despite being partially unsighted.
Davies muscled his way onto the resulting Jay Spearing corner but his header was hacked off the line by Danny N'Guessan and Millwall scrambled clear.
In a flurry of late Bolton pressure, substitute Marvin Sordell latched on to Davies' flick-on but flashed just wide.
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- Danny Shittu