George Friend scored an own-goal under pressure from John Marquis to put the Lions ahead and Martyn Woolford stole in at the back post to double their lead.
The hosts staged a spirited fightback after the break and Curtis Main grabbed a lifeline before having a second goal ruled out for a hotly disputed offside decision in stoppage time.
But Millwall held on and 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. It was a honest performance."
On Boro's late leveller which was ruled out, Jackett added: "Having looked at it I thought the one at the end was definitely offside. The officials got it right."