Weale let a back pass roll under his boot for one of the softest goals seen at Pride Park and it was enough to settle a scrappy East Midlands derby.
Shaun Barker had a superb game at the heart of Derby's defence and Leicester forced Stephen Bywater into only one real save near the end of the first half.
There was little quality in a game played on an uneven pitch and it was Weale's astonishing blunder that gifted Derby a 20th minute lead.
Paul Green poked the ball into the box and when Andy King knocked it back, Weale was under no pressure until he took his eye of it and it rolled off the bottom of his boot and into the net.
Leicester were stunned and they could have been in trouble again when Chris Porter got behind them on the right and was only denied by a sliding tackle from Jack Hobbs.
Porter opened Leicester up again in the 40th minute when he turned away from Wayne Brown but his low cross was cut out and the half ended with Bywater making a superb save to keep out a 20-yard drive from Richie Wellens.
But Leicester had rarely threatened and it was no surprise when they made a double change after Porter had fired over from the edge of the area with former Derby striker Steve Howard joining the action in the 62nd minute.
He got a good reception from the home fans but almost silenced them in the 83rd minute when his header from a corner set up Michael Morrison but his flick was straight at Bywater.
That was Leicester's last real opportunity to rescue a point and although the referee added on four minutes, Derby held on for a win that takes them closer to safety...