Goals from Alexis Sanchez and Mesut Ozil sealed the win in which Wenger switched his system from a back four to a back three for the first time in his Gunners tenure.
It provided the result the Gunners so badly needed, although it wasn't a particularly convincing performance as Wenger's team still looked vulnerable defensively at times.
At one point it looked like Arsene Wenger's side were going to drop points yet again, but a second half victor from Mesut Ozil made the scoreline 2-1, and Arsenal held on for a vital three points.
Wenger has not strayed from a traditional back four for over 20 years but made the surprise tactical adjustment for last night's trip to Middlesbrough.
'Overall I felt that it worked quite well today because we won the game.
Speaking to Sky Sports, Wenger said: "You could see we were not playing with full confidence during some moments in the game but overall we wanted to win".
Arsenal are now seven points behind fourth-placed Manchester City with a game in hand, while Middlesbrough lie six points from safety and have also played one game fewer than most of the teams above them. "I think we were so low on confidence we needed reassurance on that front".
"I felt that when we scored we had Arsenal on the back foot and at that point we just needed the ball to fall to us". "I think Middlesbrough came out second half and made it a lot more hard and they went very direct at the end but all in all it was a new system and we have got the three points with it and that is all that matters".
While unable to match Arsenal in quality, Boro managed to turn up the intensity in the second half and the hard work paid off in the 50th minute with an equaliser from Alvaro Negredo. We pushed them back, and you're just thinking the ball is going to bounce in the right area.
That win, arriving after four consecutive league defeats away from home, left Arsenal seven points behind Manchester City for the final Champions League qualifying place, with a game in hand.
Forward Alex Oxlade-Chamberlain, meanwhile, said Arsenal had gone back to basics after allowing their standards to slip.
"It's a huge honour to play for Arsenal and perhaps those amounts have stolen". "We have to take responsibility for that and we've done that this week between ourselves", he said.