Grant flapped at Ricky Newman’s hopeful cross in the last minute and palmed the ball straight at the feet of Jamie Cureton, who gratefully poked home his seventh goal of the season.
Derby appeared to have weathered the storm against a Reading side desperately seeking their first win in December and John Gregory's players looked distraught at the final whistle.
In Sammy Igoe, making his first start since September, they boasted the games outstanding player and teenage winger Nathan Tyson, making only his second start of the season, sparkled on the left wing.
It was that combination which carved out Reading’s opener inside five minutes.
Igoe ended a dazzling run with a perfect pass into space for Tyson, who showed exactly why Reading manager Alan Pardew had preferred him to John Salako, with a clinical left-foot finish for his first goal for the club.
That was Reading’s first goal in five matches, but it hardly opened the floodgates for the home side.
Instead it was Derby who provided an instant response as Lee Morris' penalty box trickery tempted Igoe into handling and presented Craig Burley with a chance to coolly drive home from the penalty spot.
Reading enjoyed the better of the possession and the better of the chances, Cureton flicking a close-range effort over the bar following more good work by Igoe and Tyson five minutes before the break.
A minute later Tyson went it alone, his stinging shot forcing a fine reaction save from the alert Grant.
Derby's chances were few and far between but Izale McLeod had the best of them on 75 minutes when he found himself unmarked just eight yards out, but managed to plant his header well over from a Burley free-kick.
The let-off prompted a late onslaught from the home side and Newman saw his shot hit the outside of a post as the home side finished strongly.
But all their efforts appeared to have gone to waste until the dying seconds, when sub SalakoÂ’s deep cross was hooked back into the area by Newman prompting panic from the previously unflappable Derby keeper.