The former England Under-21 international, who had scored nine braces prior to this evening, broke the deadlock two minutes before the break when having weaved his way into the away side's penalty area, he beat Frank Fielding with a low finish.
Ince, son of former Manchester United, Inter Milan and Liverpool midfielder Paul, then added his and Derby's second goal of the contest in the 64th minute. On this occasion the playmaker's left-footed effort squirmed beyond Fielding, who may feel that he should have done better.
The hat-trick was completed seven minutes later when having been played in by Darren Bent, he got the better of Fielding again, this time with his right foot.
Johnny Russell then got in on the act in the 77th minute when he converted Chris Baird's cross to score his first goal for the Rams since October.
The win, which is Derby's sixth in their last eight home outings, has seen Paul Clement's side remain third, two points adrift of joint leaders Brighton & Hove Albion and Middlesbrough. As for the visiting Robins, their 10th defeat of the season has left them one place above the drop zone.