Tammy Abraham scored four goals for Villa, who trailed 2-0 and 3-2 in a remarkable first half that ended 3-3.
Lewis Grabban and Joao Carvalho put Forest two goals ahead before Abraham dragged the hosts back into the match, levelling the scores at 2-2 and then 3-3 after Matthew Cash put Forest back in front.
Joe Lolley's long-range effort restored Forest's lead shortly after the break but they were soon down to 10 men when Tobias Figueiredo was shown a red card.
Abraham capitalised three minutes later, heading in from Jack Grealish's free kick to make it 4-4.
Villa took the lead for the first time through Anwar El Ghazi but Grabban's near-post finish with eight minutes remaining earned Forest a point.
Both clubs were European champions in the early 1980s but Forest are now sixth in the Championship on 31 points, two places and three points above Villa.
(Reporting by Toby Davis, editing by Nick Mulvenney)
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