The hosts were nearly ahead when Daniel Ayala's header was saved by Petr Cech but Ozil sealed the victory from close range after a lay-off from Aaron Ramsey.
Wenger said: "It was positive. In the second half on one or two occasions, I felt we could have been a bit more dominant in the air, but overall yes".
"Koscielny was the central one, pulling the strings with us both and telling us where to go, so with someone like him and his experience it makes it a lot more comfortable".
"The fact we conceded three at West Brom and three at Crystal Palace, I feel it was needed".
Laurent Koscielny, Rob Holding and Gabriel Paulista looked unsure at times, confused by their new roles in a back three.
Wenger is yet to announce that he is to sign a new deal with the Gunners after first taking over 21 years ago as Arsenal boss, with less than three months remaining on his current contract.
" "Sometimes we want to have the ball but when a team lacks confidence just to change the system can help believe something different."
Garcia eyes British Open after "better late than never" Masters win
Before I won at Merion (in 2013) I said "you're going to win majors and you're going to lose majors, but you've got to be willing to lose them".
The Gunners have not lost five successive away games in the league since 1984 and manager Arsene Wenger took significant measures to avoid that happening against Boro by playing a three-man defence for the first time since 1997.
"I think we were focussed and committed and you could see that we did not play with full confidence during some moments in the game", Wenger said.
Midfielder Alex Oxlade-Chamberlain, who shone in a right wing-back role, thanked the 2,000 Arsenal fans who journeyed to Teesside and admitted that a lack of effort had contributed to recent defeats. "We need to get a win as soon as possible and change the face of it". It's a massive honour to play for a team like Arsenal and maybe that had been slipping in the last few weeks.
"It was significant. We were in a poor situation and we needed to come back with our quality", he told Sky Sports.
"Obviously we missed an opportunity". And to see our fans travel all up the way here on a Monday night, it means everything to us for them to stick by us. We put them under tremendous pressure.
"My players were incredible", said Agnew whose side are second bottom, six points behind 17th-placed Hull City with a game in hand and a vastly superior goal difference.
"This group don't know how to give in".