First-half goals from Andy King, Ayegbeni Yakubu and Yuki Abe gave the hosts a healthy lead which they almost let slip in a goal-crazy four-minute spell in the second half, which included a Diomansy Kamara strike to finally wrap up the win.
For the visitors, who responded with second-half goals from Grant Leadbitter and Connor Wickham, it was another reminder of how much progress they will need to make in order to match the success of East Anglian rivals Norwich, who are heading for the Premier League.
Both sides had designs on the play-offs back in August but sacked their respective managers after disappointing starts, and although Paul Jewell and Sven-Goran Eriksson have each led a revival of sorts, the clubs fell some way short of their pre-season expectations.
Despite their poor run of form going into the game - just one win from their previous five matches - the hosts started in positive fashion and could have taken the lead inside the first two minutes but David Norris dragged his shot just wide from inside the box.
The Tractor Boys' first meaningful foray into their opponents' half led to a speculative long-range effort from Lee Martin, which Angelo Miguel Vitor deflected behind for a corner.
Eriksson's side came under further pressure when Wickham hammered in a low shot which Weale parried before denying Jason Scotland on the rebound.
And having weathered the storm, the Foxes seized the advantage in the 26th minute when Paul Gallagher whipped in an inch-perfect cross for King to nod home his 16th goal of the season.
City were immediately forced into a change as Kamara replaced the injured Darius Vassell.
The substitution galvanised the home side, with Kamara latching onto a through-ball - but he miscontrolled at the crucial moment as a one-on-one chance went begging.
Just before the break the home side doubled their lead when Abe's searching cross found King, whose header smashed off the post but fell kindly for Yakubu to fire in.
And there was still time for Abe to bag his first City goal, curling home a fantastic effort from 20 yards after receiving a defence-splitting pass from King.
Town signalled their intent early in the second half as Wickham rifled in a low shot which forced Weale into a fantastic save.
The pace and tempo so evident in Leicester's first-half display was conspicuous by its absence after the interval, with Jewell's side being afforded more time and space to create chances of their own.
And they were gifted the chance to gain a foothold in the game thanks to Jeffrey Bruma's inexplicable handball in the box, which allowed Leadbitter to score from the spot in the 69th minute.
Patrick Van Aanholt then showed his charitable side a minute later as he gifted possession to Wickham, who advanced into the area before reducing the deficit to a single goal.
However, the Dutchman made amends as he provided the cross which led to Kamara's 82nd-minute goal, which put the seal on a thrilling victory for the hosts.
A game which had almost everything should have seen a red card thrown into the mix late on, but Leadbitter's ill-timed challenge on Yakubu was only deemed worthy of a booking.