Both managers agree that the 30th minute dismissal of the Turkish international had thrown the game in favour of the visitors.
It was 0-0 when Tugay, already in the book for a handball offence, was given his marching orders by West Yorkshire referee Mike Riley for a rash challenge on Gaizka Mendieta.
Down to ten men, Rovers, who had been the livelier of the two sides, were always going to find it an uphill struggle.
And three Boro goals in the space of 11 crazy minutes at the start of the second half condemned Rovers to their first Premiership home defeat this season.
Hasselbaink got the ball rolling a minute after the restart with a quality finish after he had twisted passed two Blackburn challenges and four minutes later George Boateng made the most of acres of space in the home area to score number two.
Hassalbaink needed only one touch to beat Brad Friedel with a great finish from a Stewart Downing cross in the 57th minute and, with Blackburn well beaten, the ace marksmen secured his treble with another first-class goal in the final seconds.
Blackburn were unfortunate when Youri Djorkaeff first had a shot superbly saved by Mark Schwarzer before the Frenchman also had a "goal" cancelled out in a offside flat.
Blackburn has started promisingly with Paul Dickov, Brett Emerton and Barry Ferguson all going close to giving them the lead.
Tugay's dismissal knocked Blackburn out of their stride and as soon as Middlesbrough decided to increase their ambition and go for goals there was only ever going to be one winner.
The victory kept Boro firmly in the upper echelons of the table ahead of their UEFA Cup trip to Aigaleo in Greece, while Rovers are nervously looking to move away from the relegation places as quickly as possible.
Man of the Match: Jimmy Floyd Hasselbaink – The Dutchman showed just why Boro gambled on bringing him to the Riverside in the summer, netting a razor-sharp treble.