Ince joined Steve McClaren's promotion-hopefuls on loan for the rest of the season on transfer deadline day due to a lack of first-team football at Hull City and made an immediate impact at the iPro Stadium.
The former Blackpool man opened the scoring with a sublime free-kick and Jeff Hendrick scored the first of his two goals to double Derby's lead just before half-time.
Bolton almost secured a shock FA Cup win over Liverpool in midweek before two late goals consigned them to a 2-1 defeat, but they were facing a rout when Ince struck again early in the second half.
Filip Twardzik pulled a goal back with a debut goal four minutes later, but Hendrick rounded off the result and Ince hit the post late on as Derby eased to an eighth win in their last nine games in all competitions.
Derby face a trip to Bournemouth on Tuesday and Eddie Howe's side will go into that top-of-the-table clash at the summit on goal difference following their 3-1 win at beleaguered Wigan Athletic.
Leading scorer Callum Wilson scored twice and Yann Kermorgant was also on target at the DW Stadium to ensure Leon Clarke's strike on his Wigan debut was in vain.
Defeat for Wigan keeps them seven points adrift of fourth-bottom Brighton and Hove Albion, with the Lancashire side having won only one of their last 16 games in all competitions.
Middlesbrough stay a point behind the top two after goals from Patrick Bamford, Jelle Vossen and Lee Tomlin secured a 3-1 home win over Charlton Athletic.
Ipswich Town's automatic promotion hopes suffered a setback with a 2-0 defeat at Rotherham United and Brentford replaced Mick McCarthy's men in fourth spot by winning 1-0 at Leeds United, while Dougie Freedman secured a 3-2 win at Brighton in his first game as Nottingham Forest manager.
A late Odion Ighalo goal gave sixth-placed Watford a 1-0 win over Blackburn Rovers at Vicarage Road and Gary Hooper scored a hat-trick as Norwich City hammered bottom side Blackpool 4-0 to move seventh.
Wolves slipped up as they were beaten 2-1 at home by Reading, while 10-man Huddersfield Town beat struggling Millwall 3-1 despite Nakhi Wells' red card.
Sheffield Wednesday drew 1-1 at home to Cardiff City, while Fulham and Birmingham City also claimed a point apiece after they also played out a 1-1 draw at Craven Cottage.
