Benjani Mwaruwari's first-half double had put the home side in control but Stephen Hunt pulled one back just before the break.
Dave Kitson made it 2-2 soon after the restart but Hermann Hreidarsson put Pompey back in front after Papa Bouba Diop's header had been ruled out.
Nicky Shorey saw a penalty saved before Benjani completed a hat-trick and Nico Kranjcar, Sean Davis and Sulley Muntari made it seven, with the latter scoring from the spot.
Shane Long had netted for Reading in the middle of all that mayhem but Shorey's deflected fourth had no bearing on the result.
Redknapp said: "We were fantastic today. We went in 2-1 up at half-time but we should have been four up. We had completely dominated the game and they had never even had a shot.
"Their keeper made an incredible save to deny Glen Johnson and then they scrambled a goal at the other end. It should have been game over but it was game on.
"Then we gave a sloppy goal away to make it 2-2 and Papa Diop had a perfectly good goal disallowed when he was two yards onside.
"There were a few wrong decisions out there today - their penalty was a throw-in to us as well.
"But we came back at them, kept going forward and we played some great football today. There were some quality performances out there today."
Shell-shocked Reading manager Steve Coppell
He said: "I have never been involved in a game like that before. It's hard to remember anything like that either as a player or a manager.
"There were 11 goals in the game and there could have been more. There was no indication at half-time that it was going to explode into life like that.
"We dragged ourselves back into it with a five minute flurry just before half-time to keep us in contact.
"Then we got ourselves in a position where we had a chance to go on and win the game. The penalty miss was crucial and their third goal was crucial.
"It seemed as though when either side attacked it was going to end up in the back of the net."