Sol Campbell and Robert Pires struck late at the end of each half to send Arsenal into Christmas at the top of the Premiership table.
The Gunners are two points clear of Chelsea and four clear of Manchester United who play at Blackburn on Sunday.
Middlesbrough finished with ten men after Luke Wilkshire was sent off.
Arsenal boss Arsene Wenger said after the match: "We showed our squad strength and we showed the right attitude.
"We were focused, determined, solid and patient when we found it difficult to get our passing going in the first half. In the end we could have scored more.
"Sol's goal came at just the right time for us and a bad time for Middlesbrough.
"His header from a corner may not be a classic Arsenal goal. But goals like that are our reward for working on dead ball moves.
"Sol is an excellent header of the ball and he's unstoppable in those situations because of his power." Centre back Campbell could have scored a hat-trick. He nodded a 34th minute corner against the outside of a post with Boro keeper Mark Schwarzer stranded, then saw a second-half effort cleared off the line by Franck Queudrue.
His strike that counted came in first-half stoppage time.
Giovanni van Bronckhorst whipped in a free-kick and Campbell nipped ahead of Gareth Southgate to bury a diving header.
Thierry Henry and Gilberto Silva went close before Boro's fate was sealed by Wilkshire's 72nd-minute dismissal. The midfielder, already booked for a foul on van Bronckhorst, was red-carded for a tackle on Pires.
Arsenal rampaged through the closing minutes and Schwarzer had to be alert to save from Sylvain Wiltord, Lauren and Henry.
But he had no chance when Pires burst onto Henry's pass to drill home a clinical shot with time running out.
Boro have failed to score in seven of their nine away games and Alen Boksic's 17th minute shot was their only threat to David Seaman's goal.
To complete their sorry day, midfielder George Boateng was carried off with a knee injury midway through the first half.