This might be the only televised one-on-one match between both wrestlers. This looks like a it took place at the Boston Garden in 1987.
Hulk Hogan vs Ravishing Rick Rude-WWF Title by TSteck160
Pretty sure I reviewed this one on a Coliseum Video rant, but yeah, they only had a very few matches because they had heat or something. Maybe Rude airbrushed Brooke onto his tights and Hogan got jealous, one never knows.