Ryan Naderi got the crucial goal after just 10 minutes in a game of chances for Gers as they picked up another three points in the league.
There were two changes from Wednesday night’s victory over Falkirk as Dujon Sterling and Dan Neil returned, with Kosta Nedeljkovic and Cammy Devlin on the bench.
Deadline day signing Kevin Kelsy made his first appearance in a matchday squad, while fellow new addition Badredine Bouanani missed out.
That meant Rangers lined-up with Ivor Pandur in goal behind a back four of Dujon Sterling, Emmanuel Fernandez, Olwethu Makhanya and James Penrice. Dan Neil joined Nico Raskin in midfield, with the same attacking three of Findlay Curtis, Minsu and Djeidi Gassama in behind captain Lawrence Shankland.
It was the visitors who got the game underway, but there was an early blow for Gers with only 8 minutes on the clock as Shankland, who netted three times in the last two matches, was forced off with what appeared to be a hamstring issue.
Ryan Naderi came on in his place, and it was an instant impact from the 23-year-old. Motherwell’s Martin Moormann played a ball back to his goalkeeper, with Paulsen taking a heavy touch which Naderi pounced on to win.
It was a composed finish from the defender as he skipped around the goalkeeper before slotting into an empty net just four minutes after being introduced.
Djeidi Gassama was unlucky not to double the lead shortly after as he raced forward on a fantastic solo run, before cutting inside to get a shot at goal, but it was deflected wide for a corner.
Rangers were looking lively as Minsu had a header saved by Paulsen after a cross into the box from Findlay Curtis.
Alex Lowry combined with Regan Charles-Cook in the 25th minute as the visitors looked for a response. The ex-Ranger picked up on the return pass to take a touch before sending a powerful hit towards goal from inside the box, but Pandur blocked well.
Before the half-hour mark, Rangers were awarded a penalty as Duncan Nicolson pointed to the spot after Djeidi Gassama was taken down in the box by Tom Sparrow.
It was Minsu who stepped up to the spot, but the South Korean sent his penalty wide of the target.
Rangers were pushing for a second before the break as Dujon Sterling delivered an inviting cross into the box, which Gassama looked certain to head beyond Paulsen, but the goalkeeper managed to claw it away, before the danger was cleared by a defender.
The same continued in the second-half as Minsu was denied by Paulsen, before James Penrice got a connection on the rebound, which came back off the post.
Tawanda Maswanhise saw a low shot gathered by Pandur, before at the other end Moormann cleared a Nico Raskin ball off the line.
A double change came for Gers with 20 minutes remaining at Ibrox as McInnes handed a debut to Kevin Kelsy as he replaced Minsu, with Daisuke Yokota coming on for Djeidi Gassama.
Yokota had a fantastic opening minutes later after another mix-up at the back from Motherwell as a loose pass fell for the winger inside the box, but his left-footed shot was high of the target.
Kelsy was inches away from a debut goal as he sent a shot just over after getting on the end of a ball inside the box.
Ben Godfrey was introduced in the final minutes for Rangers, as McInnes’ men saw the game out to secure another three points in the Scottish Premiership.
RANGERS: Pandur, Sterling, Fernandez (Godfrey, 90), Makhanya, Penrice, Raskin, Neil, Curtis, Minsu (Kelsy, 69), Gassama (Yokota, 69), Shankland (Naderi, 8).
Subs: Kelly, McCrorie, Devlin, Dragojevic, Chukwuani. Motherwell: Paulsen, Girdwood-Reich, Moormann, Sparrow, Fadinger, Lowry (Levitt, 74), Charles-Cook (Palmer-Houlden, 63), Maswanhise (Bjorgolfsson, 84), Said (Kanga, 46), Longelo (Williams, 74), Hodge.
Subs: Connelly, O’Donnell, Knight-Lebel, Kanga, Vogt.