Manager Arsene Wenger was satisfied with the performance following the midweek draw with United at Highbury.
Wenger said: "There were some people saying after that game that we might let it go or not play so well but I thought we controlled the game against Middlesbrough.
"I thought we kept the team's shape. I always believed we would eventually score because Middlesbrough would have to come out at some stage."Wenger was cautious over the destination of the Championship. "It looks like both teams will have to go all out to win every game," he replied when asked whether or Arsenal or Manchester United would come out on top.
Middlesbrough welcomed the return after injury of George Boateng but were without the services of Geremi.
The absence of the Cameroon international, who has been linked with Manchester United, was evident as Boro's unbeaten eight-match run came to an end.
Unfortunately for the home side the on-loan Real Madrid player could be out of action for two or three weeks.
Arsenal eventually recorded a double over Boro with second-half goals by Sylvain Wiltord and Thierry Henry.
The game overall lacked drama and goalmouth thrills.
Middlesbrough never really showed the threat to upset the visitors and Brazilian midfielder Juninho had his most ineffective game since his return after a pre-season knee injury.
The all-important first goal came three minutes after the break when Henry took advantage of a mistake by Doriva for Wiltord to shoot into the corner of the net.
In the final minutes Henry crashed a magnificent free-kick into the roof of the net in front of the ecstatic Arsenal fans.
After the game Boro boss Steve McClaren said: 'I thought our back four were magnificent today while Arsenal impressed me. I could see their concentration and focus from the first whistle.
"To lose to Arsenal was no disgrace but it was not our day."