R's boss Iain Dowie was in charge of Coventry City when they knocked Carlisle out of the cup last season and steered Charlton Athletic to victory over them the season before.
This time Ledesma's second-half treble and Damion Stewart's strike were enough to seal a place in the third round and a possible tie with one of the big boys.
The hosts started brightly with Ledesma's left foot causing all sorts of trouble.
Dowie's side were slick in their approach play in the first period but lacked a cutting edge.
Ledesma looked certain to open the scoring on 30 minutes but lifted his shot agonisingly wide.
Minutes later, Ben Williams dropped Daniel Parejo's right-wing corner, but Rangers couldn't profit from the goalmouth scramble.
For all their dominance, QPR almost fell behind five minutes before the break when Simon Hackney found Michael Bridges in acres of space, but the former Leeds striker fired wide.
After a dour first half, Dowie's half-time team talk worked wonders as Stewart rose to nod home Parejo's corner on 48 minutes.
Ledesma doubled the lead on 56 minutes after turning his marker before sending a left-foot rocket into the corner.
It quickly turned into the Ledesma show on 63 minutes as Parejo's lay off found the hitman in space and he lashed it past a despairing Williams to make it 3-0.
Ledesma completed the rout and bagged a hat trick on 85 minutes after he cleverly chipped Williams to complete the scoring.