Colin Kazim-Richards opened the scoring at Pride Park a minute before half-time and Scott Dann added a second goal as the midway-point of the second period approached.
Jordan Rhodes settled the tie shortly afterwards with his 22nd goal of the season.
It was Blackburn's first victory in four games since beating Bristol City in the third round and Appleton's maiden success since taking charge three matches ago.
Derby were unchanged from the team that started last weekend's draw against east midlands rivals Nottingham Forest.
There was one change for the visitors as Joshua King was recalled. With Todd Kane cup-tied, it meant a defensive reshuffle for Appleton. Jason Lowe moved to right-back, Morten Gamst Pedersen reverted to central midfield and King played wide on the right.
King's afternoon lasted just 10 minutes before he went off injured. He was replaced by Ruben Rochina.
Both sides enjoyed periods of pressure but chances were few and far between.
However, Adam Legzdins produced a superb save after 26 minutes. Pedersen's free-kick looked certain to find the top corner but the Derby goalkeeper tipped the ball away.
A mistake by the usually reliable Richard Keogh presented Blackburn with the opening goal, when Kazim-Richards shrugged the Rams centre-half off the ball before powering goalwards and lashing a low shot past Legzdins.
Derby-born Jake Kean preserved Rovers' lead in first-half injury time, getting down quickly to save John Brayford's free-kick.
The hosts had a couple of chances to get themselves level soon after the break but Kean, a former Rams trainee, kept out a header from Brayford before tipping behind Jamie Ward's lob.
Blackburn led 2-0 in the 66th minute when Dann crashed in a volley at the far post from Danny Murphy's cross from the right.
Rhodes got his name on the scoresheet after 71 minutes. It was scrappy inside the Derby penalty area but when the ball fell to Rhodes he finished clinically from 12 yards out to ensure progress to the fifth round.