Goals from James Maxwell - his first for the club - and Kyle Hurst capped off a dominant display and ensured Danny Schofield's side began 2023 with a bang.
Rovers took just four minutes to open the scoring and enjoyed almost total control in the first half.
Hurst went close to doubling their lead prior to scoring his fifth goal of the season and first since September before Kristian Dennis pulled one back for Carlisle.
Here’s our player ratings.
1. Match action
Doncaster's James Maxwell scores the opening goal. Photo: HOWARD ROE, Howard Roe/AHPIX LTD
2. Jonathan Mitchell - 7
Didn't have a huge amount to do but commanded his box well. Saved well from Kristian Dennis after the goal. Photo: Gareth Williams/AHPIX LTD
3. Charlie Seaman - 7
Booked for a dangerous challenge that could have seen him sent off. Another lively display though. Photo: Howard Roe/AHPIX LTD
4. Kyle Knoyle - 7
Made a brilliant driving run into the opposition half and contributed to a solid defensive display. Photo: Howard Roe/AHPIX LTD