It was their fourth win in five league matches and lifted the Red and Greens up to ninth in Midlands One East.
Dan Robinson put the visitors ahead with the opening score which he converted for a 7-0 lead.
But then his kick was charged down to present the Derbyshire side with a converted try to level the scores.
But Rasen and Louth then took complete charge with winger Nick Harvey sprinting up the line to touch down in the corner and restore the lead.
Robinson then added his second try in identical fashion, from an attacking 5m scrum, to put the visitors 19-7 ahead at the break.
The Red and Greens had their try bonus point within three minutes of the restart through a Tom Stephens score after the pack turned over possession at a scrum.
An infringement reduced Ilkeston to 14 and gave Rasen and Louth a penalty which was kicked to touch. Peter Everton went over from another well-worked catch and drive routine.
Adam Dearden’s ill-advised tip tackle earned the centre a yellow card, but Rasen’s earned a further penalty kick to touch and Mills was the beneficiary of another catch and drive assault.
Good work from Ben Chamberlin paved the way for Gutteridge to get on the scoresheet before Everton put Stephens away in the corner or the final try.
* Rasen host third-placed Kettering on Saturday (kick-off 2.15pm).