United started brightly with ex-City favourite Jordan Stewart testing Chris Weale from distance in the first minute.
The home side hit back through Richie Wellens but his 25-yard drive failed to find the target. Lloyd Dyer then ran into the box from halfway but lost his balance and miscued his shot wide.
Mark Bunn twice rescued his side in less than a minute, first when he was at full-stretch to prevent Chris Morgan's back header drifting into his own net and then producing an instinctive save to stop his defender Nick Montgomery suffering a similar fate after he had sliced goalwards from Matty Oakley's corner.
Leicester had penalty claims waved aside when Matthew Kilgallon appeared to handle inside the area.
City continued to impress with Michael Morrison's 40-yard thunderbolt being tipped over by Bunn.
The Foxes took the lead from the resultant corner when Morrison timed his back-post run to perfection to head home Oakley's 26th-minute corner.
City doubled their lead in the 35th minute when Montgomery tripped Matt Fryatt inside the area and Leicester's top-scorer picked himself up to place the spot-kick low to the keeper's left for his 12th goal of the season.
City were denied a third on the stroke of half-time when Wellens rattled the bar from 18 yards.
United pulled a goal back in the 47th minute when half-time substitute Henri Camara converted Stephen Quinn's cross from close range.
Steven Howard went close twice on the hour mark, first when his turn and shot was pushed away by Bunn before he side-footed just over after a marvellous run by Fryatt.
Weale's acrobatic save kept out Jamie Ward's drive before Morgan headed wide and Camara shot over.
Howard set up Fryatt who curled an effort narrowly wide as the game flowed from end to end with City hanging on for a deserved win.