Leigertwood thundered home a rasping drive from 20 yards out after 15 minutes to put the Royals in control, and the home side coasted through the opening period before Leicester came out fighting in the second half.
However, the visitors were unable to convert any of the several chances they created after the break and with quarter of an hour remaining Jason Roberts added a second for the hosts with a six-yard tap in.
Simon Church came off the bench to head a third late in the second period and, while Neil Danns clawed one back for the Foxes, it was far too little far too late as Reading moved level on points with second-placed West Ham.
Reading started the match at a canter, with Kasper Schmeichel in the Leicester goal saving from Noel Hunt before Wes Morgan cleared off the line from Hal Robson-Kanu.
But the visiting Foxes could not hold out for long, and on the quarter hour mark Leigertwood fired the Royals in front.
Robson-Kanu picked out the midfielder on the edge of the box at the end of a flowing Reading attack, and Leigertwood produced a stunning rocket of an effort to find the top right hand corner.
Leicester slowly found their feet, David Nugent shot wide from 18 yards and Danns tested Adam Federici from distance, but the away side struggled to open up their hosts.
Reading mixed a stubborn resilience in defence with their uncanny knack to protect possession in midfield to take their one goal advantage through until half-time, but the away side started quickly after the break.
Lloyd Dyer's cross fell to the feet of Danny Drinkwater on the edge of the penalty area, but Drinkwater could not direct his effort on target before Nugent shot wide after cutting in from the left.
Nugent headed Drinkwater's corner wide after 54 minutes as the Foxes continued to pile pressure on their hosts in pursuit of an equaliser.
After being second best for much of the first period, Leicester looked dangerous and Federici had to be alert to hold on to Danns' long-range effort.
However, Reading were always likely to threaten on the counter, and the Royals thought they ought to have been awarded a penalty when Roberts was felled in the box only for referee Robert Madley to waves away their claims.
The home fans did not have to wait long for another reason to cheer, though, as Reading doubled their advantage after 75 minutes.
Hunt charged down right before taking his time to find strike partner Roberts in the box and the former Blackburn striker obliged with a clinical finish from six yards.
And Hunt was again the provider with a minute left, searching out substitute Church to nod home and, although Danns took some of the gloss off the performance with a consolation for Leicester at the death, Reading's charge continues.