Matty McNeil and Oli Johnson scored in the final 11 minutes to break 10-man Millwall's hearts and rescue a draw for spirited Stockport.
McNeil lashed home the first from close range before Johnson's deflected 20-yard strike beat David Forde.
The Lions led when McLeod beat keeper Owain fon Williams from close range.
McLeod made it 2-0 when he netted from the spot after being tripped by fon Williams but the Hatters hit back after David Martin saw red for two cautions.
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