After being frustrated by the away side for 58 minutes, Ciro Immobile broke the deadlock with a side-foot finish from the edge of the box.
That looked to have given Jurgen Klopp's side the win until Aleksandar Mitrovic rose highest to meet an Anthony Vanden Borre cross and head his side to a point six minutes from time.
The draw means Dortmund win the group on goal difference, with Anderlecht qualifying for the Europa League courtesy of a third-placed finish.
Arsenal's comfortable victory in Galatasaray meant the pressure was on Dortmund to at least avoid defeat and ideally win to head off the Premier League club nicking top spot following the final round of group games.
Klopp's team have surprisingly struggled domestically in the early stages of this season, with Friday's 1-0 win over Hoffenheim just their second Bundesliga victory in 11 matches.
In Europe, though, Dortmund have continued to thrive and appeared to be on course for a fifth win in six games on Tuesday courtesy of an inconsistent but patient performance.
The home side, who were without Mats Hummels in the centre of their defence but welcomed back midfielder Nuri Sahin for his first start since the DFB-Pokal final in May, were incisive going forward, regularly breaking through the Anderlecht back line.
The only thing that prevented the German side cruising into a game-winning lead was the presence of Silvio Proto in the away goal.
The Anderlecht number one produced a string of saves to keep Dortmund at bay for almost an hour, including two to push away shots from Immobile in the box and another to deny Shinji Kagawa's angled drive from 12 yards.
Henrikh Mkhitaryan was also twice denied, either side of half-time, as Proto proved equal to his well-struck efforts.
To compound Dortmund's frustration, with Hummels missing and Matthias Ginter partnering Neven Subotic in the centre of defence, they looked vulnerable at the back.
The hosts were indebted to goalkeeper Mitchell Langerak in the early stages when he produced a superb block from an Aleksandar Mitrovic shot after the striker had beaten the offside trap to collect a defence-splitting pass from Dennis Praet.
And Dortmund should have conceded on the stroke of half-time when Sacha Kljestan was given plenty of space and time to finish a knock-down, but the midfielder blazed his effort from 15 yards over the bar.
Much to the relief of the home team, Proto's heroics had a shelf life and 13 minutes into the second half Immobile collected a pass from Sahin, evaded a challenge on the edge of the box and stroked his shot into the net.
Mkhitaryan could have made the win safe with seven minutes to go, but, after breaking away down the right, his low shot was blocked by the boot of Proto.
This provided the platform for the attack that earned Anderlecht their equaliser and ultimately a point as Dortmund's defensive deficiencies again came to the fore.
Vanden Borre was given too much space to cross from the right and Mitrovic was too strong for his marker to head home the leveller from only his side's second attempt on target.
