The Lions led 2-0 at half-time thanks to a George Friend own goal and a Martyn Woolford effort, and then held on for the win after Curtis Main had pulled one back after the interval.
Jackett said: "It was a fantastic result and a great performance
"Middlesbrough is a very difficult place to come and get a result, so we have got to be delighted with it.
"We made a few changes and we went with two up top, and it paid off for us. The boys worked very hard for it and it was an honest performance."
Middlesbrough had what would have been a stoppage-time equaliser contentiously ruled out for offside and Jackett thought the decision was correct.
"Having looked at it, I thought the one at the end was definitely offside," he said. "The officials got it right."