The visitors took the lead early on through Lee Mills, who headed home a Graham Hyde cross, giving the Bulls a one goal half time lead.
Warren Peyton equalised just after the restart, before Hereford quickly regained the lead when former Bradford striker Mills grabbed his second of the game.
Gareth Stoker equalised almost immediately to make it 2-2, but substitute Adam Stansfield looked to have won it for the visitors with just eight minutes remaining on the clock.
However, RMI had seemingly grabbed an unlikely point when Steve Smith made it 3-3 in the last minute of normal time, but RMI's hopes were dashed in stoppage time when Stansfield grabbed his second.
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