The 17-year-old only got his chance because Nikos Dabizas was suspended but he seized his moment on 15 minutes to give City the lead.
Stephen Hughes swung over a corner which was nodded down by Patrick McCarthy for Leicester-born Stearman to lash the ball into the roof of the net from six yards.
Ian Walker kept the lead intact on 27 minutes when he was at full stretch to tip Paul Robinson's header over the bar.
Ben May then got in a looping header over Walker, but McCarthy raced back to clear off the line.
At times City looked uncertain at the back especially after Stearman limped off injured on 50 minutes and they were made to pay midway through the second half when they failed to clear a Jody Morris corner, which Danny Dichio tucked home at the far post.
But City took just four minutes to retake the lead after Matt Lawrence tripped David Connolly inside the 18-yard area. Connolly picked himself up to score with a penalty hit to the keeper's right.
A blunder by Andy Marshall put the result beyond doubt on 83 minutes when he allowed a Mark De Vries' far-post header to slip between his legs for City's third.
That was the Leicester striker's first for the Foxes and he almost notched a second when he stuck a post in the final minute.
Afterwards Leicester manager Craig Levein said: "Richard Stearman was one of our best players until he went off injured.
"He scored and was playing out of position at full-back.
"After he came off injured he was taken to hospital for x-rays for a damaged ankle and bruised cheekbone.
"We want to finish the season as strongly as we can because it is important to pick up points and play good football so our fans want to come and watch us."
Millwall coach Ray Wilkins said: "Our promotion chances seem to be drifting away.
"We needed a win or draw today to maintain our push for the play-offs, but this is a funny division and you never know what might happen."