Chris Taylor's strike midway through the second half proved the difference between the two sides at the New Den.
And in the face of considerable pressure in the closing stages, Millwall held the Foxes at bay to leave Jackett delighted.
"We had to weather the storm and we defended very well," Jackett said. "But then we started to create chances of our own and eventually made it a dominant performance.
"The goal came at the right time and gave us something to hold onto, to see the game out.
"We showed some guts, we had to be at our very best against a Leicester side who have real quality across the board.
"We defended very well in injury time, there were balls flying in all over the place but my two centre-halves handled that very well.
"Danny Shittu has been a key player for us. He played a captain's role out there and was solid at the back all day.
"Darius Henderson is coming back soon and that will help us because we need to maintain our position and push forward to build on this great start."
- Sports & Recreation