The Lions had a penalty appeal ignored after 21 minutes when Joe Mattock appeared to upend Marc Laird in the box as the midfielder tried to smash home the rebound from James Henry's initial strike.
But it was Leicester who broke the deadlock 60 seconds later when Howard smashed home a low drive from 18 yards.
Howard came close to doubling the Foxes' advantage on the stroke of half-time with a free-kick from 30 yards, but it sailed just wide of the post.
Tom Cleverley should have made it two for Leicester in the 67th minute but his shot from inside the area was pushed behind by David Forde for a corner.
Only the post denied League One's leading scorer Matty Fryatt from adding a second in the 78th minute. Tony Craig's header three minutes later tested Tony Warner, but the Lions did not trouble the visiting keeper again and Leicester comfortably ran down the clock.