Boro took full revenge for a last-gasp 2-1 defeat at Anfield in their first away game of the season and a vital three points before a sell-out crowd are a tremendous boost to their relegation fight.
No wonder the jubilant home fans gave the team a standing ovation at the final whistle.
The Riverside Stadium does not rank among Liverpool's favourite grounds. Indeed, it has been a hoodoo ground for them in recent years.
On their last six visits, Liverpool have scored only one goal - from Fernando Tores last season.
Middlesbrough enjoyed a rare slice of luck this season when Liverpool midfielder Xabi Alonso put through his own goal in the first half.
They followed up with the second-half goal by Tuncay and overall deserved their triumph.
Liverpool dominated in the early stages of the game, but failed to take advantage and paid the penalty against a Boro side that kept their balance and won a tremendous number of tackles.
Manager Gareth Southgate must have been highly delighted with the performance of his team that rounded off a successful week in which the Boro knocked West Ham out of the FA Cup.
Middlesbrough goalkeeper Brad Jones brought off a brilliant save from Dirk Kuyt in the early stages and later denied Ryan Babel.
Liverpool played the more controlled football in the opening stages with skipper Steve Gerrard, recalled after injury, pushing and probing from midfield.
Against the run of play Boro went ahead after 30 minutes when Stewart Downing put over a right-wing corner. Alonso stuck out a leg and saw the ball go past the outstretched hand of goalkeeper Pepe Reina.
Middlesbrough had struggled to make headway before this break, but the goal boosted their confidence.
It was expected Liverpool would throw everything but the kitchen sink after the break but the visitors wasted early chances. Martin Skrtel blasted wide from 25 yards and Nabil El Zhar wasted the best scoring chance by shooting over the bar from eight yards.
Middlesbrough kept their balance and composure and began to raise hopes of a coupon-busting win.
A second arrived after 62 minutes. Jeremie Aliadiere provided the pass and Turkey international Tuncay provided the finish.
Tuncay raced to a corner flag to share his joy with home fans and was promptly booked for taking off his shirt.
Liverpool's hopes of pulling the game round virtually disappeared when Gerrard and Jamie Carragher were substituted within five minutes of each other.
Middlesbrough, the lowest scorers in the Premier League, will take heart from a battling performance after a 14-match league run without a win.