The hosts dropped down to eighth following wins for Brighton and Hove Albion and Ipswich Town at the weekend, but earned a point against the leaders on Monday to boost their promotion hopes.
Alex Pearce gave Nigel Adkins' side the lead after 16 minutes but Danny Drinkwater hit back for the visitors before half-time.
Reading, who are now winless at home in seven league matches, saw second-half substitute Mikele Leigertwood sent off for a second bookable offence late on but, despite five minutes of stoppage time, Leicester could not find a winner.
Pearce's early back-post header put Reading on the right track for a first victory at the Madjeski Stadium since January, but they were pegged back 12 minutes before the break.
Drinkwater's powerful drive from distance found its way through a crowded area and sailed past a motionless Alex McCarthy in the hosts' goal.
There was little to choose between the two sides after the interval and Leigertwood's dismissal in the 86th minute - having only been introduced on the hour mark - did not prove costly for Reading.
With second-placed Burnley having lost at home to Middlesbrough on Saturday, Nigel Pearson's men - who have already secured promotion - actually extended their advantage at the summit to seven points with four games remaining.
