Leicester could have been two up inside three minutes as first Matt Fryatt picked up a misdirected pass from Yeovil's Nathan Smith but put a clear chance over the bar.
Almost immediately he was in the action again as this time he found the target but keeper Josh Wagenaar made an excellent block and Matt Oakley put the rebound over the bar.
Yeovil, already without two top players through suspension, lost their influential midfielder Gary Roberts in the tenth minute.
He trod on the ball and there were fears he had broken a leg, but the eventual diagnosis was ligament damage, which will keep him out for four to six weeks.
Leicester continued to look for a goal and on 28 minutes almost broke the deadlock when Lloyd Dyer picked out Steve Howard at the far post but the big striker headed against the top of the bar.
Three minutes later, Howard was clear but denied what might have been a goal by a dubious offside flag.
It was a refereeing decision at the other end soon after half-time that angered Yeovil and led to the opening goal.
The referee gave the Foxes a corner with Yeovil insisting it should have been a goal-kick.
The flag-kick on the right was worked across the pitch to Mark Davies, who crowned an outstanding display in midfield by picking out Howard, who scored from 15 yards.
Luke Rodgers battled bravely up front and made some intelligent runs in an attempt to get Yeovil back on terms, but Leicester defended well and goalkeeper Dave Martin did not have a real shot to save.
Six minutes from time, Leicester boss Nigel Pearson introduced loan signing Tom Cleverley from Manchester United for his debut and he was an instant success, laying on the clincher three minutes from time for another sub, Joe Mattock.
His fierce drive gave Wagenaar no chance and Leicester deserved the victory which stretched their unbeaten run to 12 matches and left Yeovil perilously close to the relegation zone.