The Foxes' hopes of a top-six finish had been hurt by a run of three defeats in four matches but they returned to winning ways in emphatic style thanks to goals from Portuguese defender Vitor (31, 72) and Kyle Naughton (76).
Scunthorpe are desperate for points at the other end of the table but, although Joe Garner came close to giving them an early lead, they were second best and remain four points from safety.
It was the Foxes who settled the better on a poor pitch, with Paul Gallagher's early cross from the left hooked just over the crossbar by Darius Vassell.
But Scunthorpe, who have revitalised their survival bid with three wins in the last month, possibly should have taken the lead after 12 minutes when Garner's header from a corner was cleared off the line by Richie Wellens.
Scunthorpe goalkeeper Josh Lillis was called on to make a decent block when Naughton's long throw was allowed to travel all the way to Ayegbeni Yakubu four yards out, and in the 31st minute the Foxes deservedly took the lead.
It all stemmed from a terrific 25-yard shot from Yuki Abe that thundered off the crossbar, with Michael Nelson doing well to head the rebound off the line under pressure from Yakubu.
Sol Bamba's effort was then deflected behind for another corner, from which Leicester found the net. Gallagher's delivery was guided towards the back post by Ben Mee and defender Vitor stabbed in his second goal for the club.
It looked set to be a dream start to the second half for Scunthorpe when referee Rob Shoebridge pointed to the penalty spot for a push by Naughton on Garner, but a glance towards his assistant revealed the striker had been flagged offside and the decision was reversed.
Gallagher then tested Lillis with a curling free-kick, while a breakaway in the 59th minute should have resulted in a second goal for Leicester but leading scorer Andy King could not quite stretch far enough to turn Vassell's cross into an empty net.
Having had a penalty taken away, the hosts saw a goal chalked off in the 67th minute, with Garner booked for handling the ball over the line.
Scunthorpe's challenge was all-but ended in the 72nd minute, though, when a peach of a right-wing cross from Gallagher was headed in off the crossbar by Vitor.
Four minutes later, Leicester had their third as a short free-kick from Gallagher caught out the home defence, allowing Naughton to curl in a precise shot.