Dunne probably did not mean to catch Tuncay, who had met Chris Riggott's pass on the edge of the area, but he did foul the Turkish striker and referee Phil Dowd was right to send him off.
Downing made no mistake from the spot and Boro were on their way. They did not look back.
Isaksson, who is also expected to be leaving City after a frustrating season spent mostly as a substitute, made the first of several top-class stops when he denied Alves from close range but the Brazilian was soon on the scoresheet.
His compatriot Rochemback found him in space in the area and Alves made no mistake with his finish.
By now City's defence was nowhere to be seen and only another brilliant stop from Isaksson kept out George Boateng's shot at the far post.
Interview: Manchester City boss Sven Goran Eriksson
Downing put the game beyond City's reach with a superb volley before Alves made it 4-0, sprinting clear and finding the net despite the best efforts of Isaksson and Gelson Fernandes.
Adam Johnson came off the bench to score with a shot that span home off City defender Michael Ball and Rochemback smashed home his side's sixth goal with a powerful free-kick into the top corner.
Aliadiere came on for Tuncay and made it 7-0 by shooting into the far corner and, although Elano did manage a consolation for City when he cut inside and curled his shot past Mark Schwarzer, it was only fitting that Boro had the last word.
It was Alves who completed the rout, and his hat-trick, when he was again left all alone to fire past the helpless Isaksson.
Middlesbrough manager Gareth Southgate: "It was a great performance to say goodbye to our fans.
"The circumstances at City may have made things difficult for them and it was a massive uphill task once Richard Dunne has been sent off.
"Dunne did not mean to bring Tuncay down but I don't think the referee had a lot of choice but to send him off."
Manchester City manager Sven-Goran Eriksson: "It is difficult to take whenever you lose. But, when you lose like this, it is awful.
"To concede a penalty and have Richard Dunne sent off was a bad start but we were in the game until it was 3-0.
"After that, mentally we had nothing left. We were not even on the pitch - the team had totally gone and it was embarrassing for everyone."
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