A melee followed the dismissal and Jason McAteer was always at the centre of the trouble.
First he confronted Jorgensen and then had a face-to-face clash with Blackpool manager Simon Grayson.
The referee then red-carded McAteer despite extensive protests from Rovers boss Ronnie Moore. The referee also yellow-carded Chris Shuker for his part in the scene.
Blackpool had a dream start thanks to a dreadful ninth minute clearance from Rovers keeper Gavin Ward.
His throw hit Blackpool striker Keigan Parker on the back and he turned around and lashed a shot straight past Ward.
Rovers tried hard to put inexperienced Lewis Edge - making his debut in the home goal - under pressure.
Edge could do nothing about Calvin Zola's volleyed equaliser after a neat flick into the box from Gareth Taylor.
The best move of the game ended in Blackpool's second on 36 minutes. The ball was swept out of defence and ended with Wes Hoolahan turning his marker inside out before crashing a shot past Ward from ten yards.
The ever-dangerous Zola struck again in the 47th minute when the Blackpool defence was caught at sea.
Zola's first effort was clawed away by Edge but the striker gave the young keeper no chance from the rebound.
The red card sequence ended with Rovers frantically packing their defence in a bid to grab a draw.
Blackpool piled men forward and in the 73rd minute Ian Evatt crossed into the box and Andy Morrell headed the goal which keeps the Seasiders firmly in promotion contention.