The Dons hit the woodwork twice in Saturday's League One clash at stadium:mk before 40-year-old player/coach Rae and Brighton's Arismendi were given their marching orders on the stroke of half-time for violent conduct.
The hosts controlled the first half and Adam Chicksen lobbed wide after keeper Peter Brezovan had sliced his clearance, while Daniel Powell's deflected shot narrowly missed the target.
Dons midfielder Luke Chadwick then blasted a dipping half-volley against the crossbar and debutant Charlie Collins curled a 12-yard shot against the post following Powell's fine run.
Rae and on-loan Stoke midfielder Arismendi were sent off three minutes into first-half stoppage time for trading blows after the Uruguayan's penalty appeal had been waved away.
Chicksen drilled a shot inches wide from the edge of the box moments after the break before Seagulls full-back Gavin Hoyte was denied from close range by Dons keeper Stuart Searle as the visitors took charge. Brighton piled forward in the closing stages but Chris Holroyd, substitute Marcos Painter and Tommy Elphick were all narrowly off target as the Dons hung on for a point.