Zaine Francis-Angol's strike (69) appeared certain to send Motherwell above their visitors after Stephen McManus (47) and Aberdeen debutant Adam Rooney (67) had exchanged goals.
But Anderson bundled a scruffy equaliser well past the 90-minute mark to maintain his side's one-point advantage.
The defender suffered an early bloodied nose but managed to see the game out - unlike Aberdeen's Ryan Jack and the home side's Fraser Kerr, who both left the field on stretchers.
Jack was injured in a challenge with Shaun Hutchinson early in a lively first half which might have brought goals for both teams.
James McFadden was denied a Motherwell opener by Jamie Langfield, while at the other end Gunnar Nielsen kept out Johnny Hayes' shot and saw Barry Robson strike a post.
McManus headed Motherwell in front from Lionel Ainsworth corner, but mounting pressure from the visitors brought a debut goal for Rooney, poached on the rebound after Niall McGinn's shot came back off Nielsen.
Francis-Angol beat team-mate John Sutton to Henri Anier's cross to restore the lead only for Anderson to get the final touch on a knock-down with the clock showing 93 minutes.