Hull made a flying start to the match and took the lead inside 30 seconds, Aaron McLean the man who caught the hosts snoozing.
Things went from bad to worse for Rovers, and they found themselves two behind after just 10 minutes courtesy of a Jay Simpson strike.
The League One side responded, getting a goal back through Dave Syers on the half-hour mark to send the two sides into the break at 2-1.
Rob Jones levelled the sides just before the hour mark as Hull struggled to build on their blistering start. Paul McKenna then saw a red card to reduce the Tigers to 10 men with just over 10 minutes left.
Rovers needed all of the remaining time to find their winner, but eventually Syers converted again to complete a dramatic comeback.