The loss means the team from Lancashire falls to eighth in the table while the Tigers, who had injured England star Billy Vunipola in attendance, have a perfect record, winning six out of six so far this season.
Nutt had initially given the visitors a three-point lead, but the hosts pace amongst their back allowed them to overrun Rossendale, scoring seven tries in total.
Henri Packard scored a hat-trick, Jamie Broadley added two while Tom Outram and Frank Wragg made up the total with their single scores.
Mark Ireland completed the Tigers scoring with 21 points, made up of six conversions and three penalties.
Rossendale showed fight late in the day, with Ryan Mckibbin crossing first after a pick up from the back of the scrum.
Nutt then intercepted a pass late on to run nearly the full length of the pitch to touch down. The fly-half though failed to convert either score.
Rossendale will look to get back to winning ways next Saturday when they face Lymm on home turf, where they are unbeaten so far this season with two wins from two.
Their visitors sit one place and one point above them in the current standings, meaning the Lancashire team would leapfrog them with a victory.
Geoff Lightfoot.