It was the Rams' 11th home defeat of the season.
Veteran midfielder Savage will leave the club at the end of the season and is expected to retire after not being offered a new deal by manager Nigel Clough.
And the Welshman, who was making his 600th start of his club career, was unable to mark his final Pride Park appearance with a win as goals from Jon Stead and Cole Skuse gave the Robins a comfortable victory.
Savage was given a standing ovation when he was substituted five minutes from time but he was not at his best in a poor Derby display.
Neither side had anything other than pride to play for but a drab display from the Rams showed why Clough is planning to shake up his squad in the summer.
The Robins were in front just five minutes in when Stead turned sharply in the box and fired in a left-footed strike that on-loan Rams goalkeeper Brad Jones allowed to squirm under his body and into the net.
Derby made a positive response to that early setback and after a swift attacking move Stephen Pearson set up Theo Robinson, but the on-loan striker's right-footed finish was kept out by City keeper Dean Gerken.
Steve Davies was also denied by Gerken after the forward turned and tried his luck with a drive from the edge of the penalty area.
Derby were missing influential centre-half Shaun Barker, who had a knee operation this week, and looked vulnerable at the back as Stead raced away before firing into the side-netting.
Savage was booked for a foul on Brett Pitman, much to the delight of the Robins supporters.
Alberto Bueno tried his luck just before half-time but the Spaniard's deflected effort was tipped around the post by Gerken.
Robinson then spurned another chance to equalise, firing wide after being picked out on the edge of the penalty area.
John Brayford could have celebrated being named Derby's player of the year with a goal, but the former Crewe man drilled a shot wide after bursting forward from right-back.
But it was City who scored the second goal after 66 minutes after some terrible Derby defending.
Gareth Roberts failed to control the ball and was robbed by Pitman and the ball fell nicely for midfielder Skuse, who drilled home from 20 yards with his right foot.
The goal was greeted with a chorus of boos from the home supporters and it almost went from bad to worse for them but Albert Adomah's strike flashed wide.
Savage could have marked his final Pride Park appearance with a goal but the Rams skipper fired over from just outside the area and that proved to be one of his final contributions.
Pearson came close to a late consolation but the Robins were worthy winners.