An early first-half blitz saw the Millers - who eased past Rovers 2-0 in the league ten days earlier - race into a 3-0 lead courtesy of goals from Mickel Miller, Freddie Ladapo and Hakeem Odoffin, whose shot rebounded off the back of home keeper Louis Jones and went in after hitting the bar.
A maiden goal for the club from Will Grigg - a deadline-day signing who snubbed an offer from Doncaster - provided gloss on his debut early in the second half and further goals arrived from debutant Jake Hull, his first for the club and Joe Mattock on a night when the Millers made eight changes and helped themselves to their biggest derby win over Rovers.
On Grigg opening his account on a night of major positives, Warne said: "I thought Griggy was excellent. Hopefully, people can see why I brought him to the club.
"His hold-up play and link play was really good and he causes problems in the air and I thought Freddie (Ladapo) played really well and caused a threat in the air.
"His goal was great for him and then there was Joe Mattock scoring and Jake Hull was excellent and got a goal. Although he was way too honest and said: 'I headed it, gaffer, it hit my back and hit someone else and went in.' I said: 'don't worry about the something else.'
"I thought T (Tolaji Bola) was excellent down the left before tiring a little bit and Haks (Hakeem Odoffin) has got a full game under his belt which is good and I thought Sads (Kieran Sadlier) was pretty outstanding in the first half.
"I am obviously really pleased. We probably rode our luck to keep a clean sheet, but we made loads of changes.
"The lads needed some minutes in them in a competitive game and Richie (Wellens) picked a really competitive team and it is nice to think we can make changes and still put on a really good performance.
"I am not going to say I am not happy with a 6-0 win because I am! On another day, we could have scored more, but conceded more. From our point of view, it was a pretty good day at the office."