"It was important to keep the run going," said Boro boss Tony Mowbray whose team sit third in the Championship.
"Sometimes an international break can change momentum but we've been winning on the road this season and we managed to come here and keep it up.
"It's always good when someone who you don't expect to score pops up with one and I'm delighted for Bails (Nicky Bailey) and delighted for Joe Bennett with all the talent he possesses.
"I think we've based our season so far on good performances and good football.
"At times, we're happy to let the opposition have the ball and try and wait for the change in possession.
"I thought we were disciplined and we got our rewards for hard work and organisation."
"It was a frustrating afternoon, very much so," said Burnley boss Eddie Howe. "I thought it was a poor performance from us.
"I've said in previous weeks that we've been unlucky and have deserved more out of games but today we didn't.
"We were beaten by the better team and we didn't get off to the best of starts when we conceded quite early and Middlesbrough frustrated us.
"We're disappointed with the first goal from a number of angles and you give yourself a mountain to climb when you go one down.
We felt it was a free kick but it wasn't given.
"I just felt we weren't in control in the first half so we made a change and tried to match them up.
"It gave us more of a foothold in the game but we never looked at any stage like breaking Middlesbrough down."