Steve Bruce's team were better in every department and would have won more convincingly with better finishing.
Derby's miserable afternoon was completed by the sending off early in the second half of defender Claude Davis for an elbow in the back of Marcus Bent's head which earned him a second yellow card.
But the home side were struggling before the Jamaican's dismissal and the stark facts are they managed only one effort on target - a poorly struck free kick from Laurent Robert who was a big disappointment on his return to English football.
Robbie Savage was made captain but was well off the pace and was unable to exert his customary abrasive influence on the midfield which was dominated by Michael Brown and Denny Landzaat.
No doubt Derby's new signings will improve the team with time, but that is something manager Paul Jewell's side does not have and Championship football next season now looks certain.
Wigan have a good chance of staying up on this showing and the only concern for Bruce was the missed chances which would have cost them against a better team.
Antonio Valencia tormented Derby down the left but missed a sitter a minute before the break when he dragged a shot wide from eight yards with the goal gaping.
Bent was also outstanding but he should have done better when he fired over from ten yards after Valencia had set him up.
Derby were relieved to still be on terms at half-time but they never put any real pressure on the Wigan defence and the visitors continued to control the game.
At least Derby looked like holding out for a draw, but once again they were floored by a late goal.
Sibierski had only been on the pitch for a minute when Bent cleverly headed the ball down to him and his right-foot shot from 20 yards found the bottom right corner of Lewis Price's net.
The young goalkeeper could not be faulted and had kept his side in the game with one first-half save from Brown.
But it is now 13 games since Derby managed a clean sheet and little wonder that Jewell is trying to sign a new centre half.