Ryan Naderi’s goal was the difference in what was another strong display from McInnes’ men.
The manager named an unchanged team from last week’s 3-0 victory in the Premier Sports Cup.
That meant Rangers started with Ivor Pandur in goal, behind Dujon Sterling, Emmanuel Fernandez, Olwethu Makhanya and James Penrice.
Captain Dan Neil, who scored twice last Sunday, was in midfield again alongside Nico Raskin, while Minsu and Djeidi Gassama provided the support for strikers Kevin Kelsy and Ryan Naderi.
It was the first meeting of the Old Firm in the Scottish Premiership this season, with fans turning out in their numbers to give Gers a send-off at Ibrox as they headed across the city.
Celtic thought they had the breakthrough with only six minutes on the clock as a free-kick was headed by Scales into the path of Auston Trusty, who sent a right-footed finish beyond Pandur, but the linesman immediately raised his flag for offside.
There was pressure from the home side in the opening 20 minutes, but Gers were growing into the game as they created a few chances. Gassama drove down the left and cut back to Dan Neil on the edge of the box, but his strike was comfortably gathered by Sinisalo.
Neil turned provider minutes later, as he lifted the ball into the box, with Naderi sending a glancing header towards goal, but again it was comfortable for the goalkeeper.
At the other end, Tierney had a left-footed strike from distance which drifted just over the bar.
However, it was Rangers who took the lead with 33 minutes played at Parkhead. From the first corner for the Gers, Penrice whipped an inviting ball into the box, which eventually broke for Minsu on the edge of the area. He released a powerful hit towards goal, which Sinisalo was only able to push away, and Ryan Naderi was on hand to calmly finish his first goal in this fixture.
It should’ve been 2-0 to McInnes’ men minutes later, but Gassama was denied by the woodwork as he lifted a shot over Sinisalo, before Kelsy’s rebound effort was blocked.
Into the second-half, Ivor Pandur pulled off an incredible save just 30 seconds after the restart. A ball into the box from Mika Baur made its way to the back post where Donavan looked certain to find the back of the net with a header, but Pandur got a strong hand to push it away.
Penrice almost doubled the advantage, with another shot which Sinisalo pushed away before Sterling sent a good delivery into the box, but Naderi was unable to keep his header on target.
Gers looked lively, as Minsu came close as he carved space for himself to get a low strike towards goal, but it bounced just wide of the post.
Dan Neil looked to find Naderi at the back post with a neat cross after another good bit of build-up play from Rangers, but Sinisalo did enough to touch it out of the path of the striker.
McInnes turned to his bench for the first time with just over 20 minutes to be played as Badredine Bouanani and Findlay Curtis came on to replace Djeidi Gassama and Minsu.
With 75 minutes played, Rangers thought they had a second goal after a fantastic hit from Makhanya from the edge of the area, but it was disallowed for a handball by the defender as he got the ball under control.
Ben Godfrey was next to be introduced by McInnes as he replaced James Penrice for the final period.
Gers were still threatening, as Curtis saw a shot saved, before Raskin came close as his cross almost sneaked in at the back post, but it finished 1-0 at Parkhead as Rangers took the three points.
RANGERS: Pandur, Sterling, Fernandez, Makhanya, Penrice (Godfrey, 76), Neil (Chukwuani, 88), Raskin, Minsu (Curtis, 70), Gassama (Bouanani, 70), Kelsy (Devlin, 88), Naderi.
Subs: Kelly, McCrorie, Dragojevic, Miovski
Celtic: Sinisalo, Donovan, Carter-Vickers, Trusty, Scales (Mheuka, 89), Tierney (Tounekti, 70), McGregor, Baur, McCowan (Hogh, 46) Nygren (Forrest, 63), Duran (Hassan, 70).
Subs: Johnstone, Oxlade-Chamberlain, Murray, Ralston