The Teessiders showed superb all-round commitment for the entire 90 minutes, and their strong tackling and tenacity prevented the Gunners from displaying their usual brand of free-flowing football.
Boro have struggled in the opening months of the season with manager Gareth Southgate under pressure and the team locked in a relegation battle.
However, on this display they should soon start to climb the table and extend their stay in the top-flight.
Arsenal have not had a happy time in the north-east this week with this result coming only four days after their 1-1 draw at Newcastle United.
The visitors were strangely out of sorts and Tomas Rosicky's stoppage-time consolation effort was their only serious shot on goal.
Manager Arsene Wenger must have been bitterly disappointed with his side's dismal performance.
In contrast, Southgate can only have been delighted. The "only one Gareth Southgate" chant from home fans in the second half must have been sweet music to the beleaguered manager.
Middlesbrough included reserve team goalkeeper Ross Turnbull in their side as Mark Schwarzer was still on the injured list.
Arsenal suffered an early blow when England winger Stewart Downing gave Boro the lead from the penalty spot.
Ironically, former Arsenal player Jeremie Aliadiere was involved in the incident that led to the penalty being awarded. Kolo Toure brought down the Frenchman and Downing claimed his fourth goal of the season.
Arsenal were completely ineffective in the first half with Turnbull having a quiet time.
Boro had done a brilliant job closing down the Gunners before the break and Wenger must have hoped for a big improvement in the second half. However, Middlesbrough continued to impress with their tackling and movement after the interval.
Skipper Jonathan Woodgate was replaced by Germany international Robert Huth after 62 minutes and the Teessiders almost immediately increased their lead.
After Manuel Almunia had pushed out Gary O'Neil's shot, Tuncay pounced with a great finish from a narrow angle.
It was just reward for the Turk's tremendous running over the 90 minutes and was his second goal in two matches after his effort at Reading last weekend.
Rosicky pulled a goal back for the Gunners with virtually the last kick of the match but it was far too little and too late for the well-beaten visitors.