The Blackpool fighter was making the second defence of his Lonsdale strap at the Bowler's Arena in Manchester, but was made to work hard for the unanimous 12-round decision.
Carslaw started well and did not allow Rose to settle into any sort of rhythm during the tactical early exchanges.
A nasty cut to the Scottish challenger's scalp threatened to stop the bout in the third round after the two fighters had accidentally clashed heads.
However, the referee allowed the fight to continue as the blood that poured from the wound was not obscuring Carslaw's vision.
Carslaw proved to be a tricky customer for Rose, who looked sluggish after nine months of constant training.
Despite a busy performance, the Paisley man was only able to land glancing blows on his opponent, with the cleaner punches coming from Rose.
In the end, all three judges gave Rose the nod after the fight went to the scorecards.