The travelling Gunners uncharacteristically started with three defenders from the start, and were under the cosh early as a bright start from Boro saw them fire three shots goalwards in the opening 15 minutes.
Arsenal soon found their stride, but needed a set-piece to open the scoring three minutes from the break, Alexis Sanchez stepping up to net an exquisite free-kick from just outside the box to put his side in front.
The relegation-threatened hosts were level five minutes into the second period however, Stewart Downing’s delivery from deep finding Alvaro Negredo who left his marker to poke the ball home.
Boro almost took the lead soon after, save for a Petr Cech goal-line block to deny the hosts from close range.
The Gunners looked more likely to score as the half wore on, and did so on 70 minutes, Sanchez’s teasing ball chested down by Aaron Ramsey as an on-rushing Mesut Ozil fired the ball into the back of the net to restore his side’s lead.
Arsene Wenger’s men survived the last 20 minutes to secure the three points and leapfrog Everton into sixth, seven points adrift of fourth-placed Manchester City who have played a game more. Middlesbrough remain 19th as their top-flight woes continue.