Drew Talbot gave the relegation-threatened hosts an early lead but James O’Shea equalised early in the second half while Dons could have won it but for Lee.
Chesterfield had won four of their previous five home games and were in front after just four minutes when a cross to the back post was cleared only as far as Talbot, who smashed in a right-footed shot from 12 yards.
It could have been two-nil seven minutes later when Jack Lester got away but his shot was pushed behind by David Martin and the Dons slowly worked their way back into the game, Charlie MacDonald forcing Lee into a diving save in the 23rd minute.
The visitors replaced Jabo Ibehre with Daniel Powell for the second half and the substitute almost struck in the 49th minute but was denied by Lee, who kept out his low shot before then blocking a drive by O’Shea.
But Lee was finally beaten in the 56th minute when O’Shea ran at the home defence and drilled a 20-yard shot inside the ‘keeper’s left-hand post. Lee denied Powell again and sub Robert Hall rattled the crossbar as the Dons pressed for a winner but Chesterfield also had their moments in an end-to-end finish.