Matt Fryatt had given the Foxes the lead in the 16th minute after a blunder by Leon Barnett.
But after earlier hitting a post, Steve Howard put Town on level terms in the second period with his 101st goal for the club.
With a point apiece looking likely, O'Grady sealed the win when he touched home fellow substitute Andrew Welsh's cross-shot from the left late on to ease Leicester's relegation worries.
As well as the defeat, Luton were handed a further blow with a sixth minute injury to Kevin Nicholls let left the Town skipper using crutches after the game.
The clash was given extra spice due to the interest shown by Leicester in Luton boss Mike Newell and it was Newell's side which pushed forwards first when Howard hit a half-blocked shot at Paul Henderson from the edge of the area in the second minute after Carlos Edwards' cross.
Town though were dealt an early blow when skipper Nicholls limped off in just the sixth minute after a crunching tackle on the edge of his own penalty area.
David Bell came on and with Luton reorganising, Leicester seized on their opportunity and dominated proceedings with Richard Stearman twice firing wide and Iain Hume testing Marlon Beresford with a 14th minute 25-yard drive.
The Hatters continued to look all at sea and it was no surprise when the visitors took the lead in the 16th minute.
Gareth Williams played a hopeful long ball over the top and Barnett clumsily stumbled to the ground leaving Fryatt with the simple task of running through and slipping the ball past a hopelessly exposed Beresford.
As the home supporters made their frustrations known, Luton eventually woke up and almost conjured up an equaliser when Edwards' left-foot cross from the right fell perfectly for Howard six yards out, but the big striker saw his header bounce back off the post.
Warren Feeney came on for the ineffective Rowan Vine at half-time and the switch paid immediate dividends as the ferreting Irishman unsettled the Leicester defence.
Firstly Howard placed a far post header at Henderson after Edwards' 48th minute cross and Feeney himself then fell under Stearman's challenge in the box after Bell's slipped pass, but nothing was given.
Luton kept up the pressure and levelled in the 53rd minute when Chris Coyne flicked on Paul Underwood's corner and Howard forced the ball home with a six-yard diving header for his 13th of the season.
Leicester reminded Town of their own threat up front when Fryatt tested Beresford from 20 yards in the 61st minute and four minutes later Bell had to be alert to hack the ball out of the goalmouth after Stearman's header from a Joey Gudjonsson corner.
Gudjonsson saw a 76th minute free-kick saved by Beresford and another Barnett slip led to Foxes substitute Welsh shooting wide before O'Grady's late winner.