The win moves Wenger's men back to within seven points of the top four, while Boro are still five points from safety with just five games remaining.
The result leaves Arsenal in sixth position, seven points behind fourth-placed Manchester City who have played one match more.
Arsenal midfielder Aaron Ramsey has echoed his manager's remarks, confessing they will have to drastically turn around their form to finish in the top four.
When asked if the back-three ploy had worked, Wenger said: "Yes, it is the first time in 20 years".
"We like to dominate the ball, but when the team lacks confidence it's good to change to a system and do something different". Against Palace and West Brom, we had 70 per cent of the possession and we lost.
"I felt that it added a bit more stability on the long balls". I thought in the first half it was tight because they defended very well and we were tested just after half-time because it came back to 1-1 and then we were tested mentally and we found the response we needed and that's what we wanted. "It'll come back slowly but it had been really crucial that you win". You could see that one some occasions, we were a bit over-cautious tonight.
"There are more points to play for and nobody in the bottom three is pulling up trees and running clear.you have to keep believing". "We knew we'd face a direct game and recently we've been punished on that", Wenger told Sky Sports. "I feel overall it is not a long-term plan, but punctually it can work".
Mesut Ozil's volley earned Arsenal all three points and breathed life into the visitor's flagging hopes of Champions League qualification, after Alvaro Negredo had cancelled out an Alexis Sanchez free-kick. Second half we gave away some risky situations in our box, but overall it gave us a bit of reassurance and that's what we need at the moment.
Caretaker Boro boss Steve Agnew said: "This is a missed opportunity for us and we realise the size of the task ahead".
The likes of Ozil and Sanchez were finding it tough to break down the home side's defence, although Oxlade-Chamberlain had a lot of joy down the right flank.