The fiery Scot blasted the spot-kick down the middle to fox his former team-mate Ian Walker.
It was a scruffy and scrappy quarter-final with the Championship side showing little ambition and appearing to settle for a draw from the first whistle.
When a third-minute free-kick from Pedersen crashed against the Leicester crossbar the visitors probably thought it would be their lucky day.
They got men behind the ball in numbers at every opportunity to make it a frustrating afternoon for Rovers who failed to reach the heights they have set in recent games.
The busy Dickov twice went close and a shot on the turn from David Thompson whistled over the bar.
Substitute Jonathan Stead managed to get the ball in the net in the 68th minute but the referee had already blown up to award a free-kick for Rovers, much to the dismay of home fans.
It looked as though Leicester would hold out for a draw and take the tie into a replay but Dickov had other ideas, the crucial penalty his tenth goal of the season.