It was a hard-fought three points in the north-east, as the skipper stepped-up to the spot with 20 minutes remaining to secure the 1-0 victory.
There were four changes from midweek as Minsu Kim came in for his Rangers debut, alongside Findlay Curtis, Cammy Devlin and Lawrence Shankland.
Rangers started with Ivor Pandur in goal behind a back four of Dujon Sterling, Emmanuel Fernandez, Olwethu Makhanya and James Penrice.
Cammy Devlin came into midfield alongside Dan Neil, while Minsu Kim, Djeidi Gassama and Findlay Curtis provided attacking support for Lawrence Shankland.
It was Aberdeen who got the match underway, and there was an early opportunity from a free-kick for the hosts. The ball was swung in towards the back post by Connor Ronan, with Dan Happe unable to keep his effort down.
The home side looked lively in the opening few minutes as Olusanya caused problems for the Rangers defence and played in Mitchy Ntelo who curled a shot towards goal which was comfortably gathered by Pandur.
In his first appearance for Gers, Minsu was looking to impress and had an early sight at goal taking on a shot from the edge of the box, but it was held by Marius Muller.
Djeidi Gassama was unlucky shortly after as his strike from the edge of the area looked to be goal bound but was deflected wide.
McInnes’ men were ramping up the pressure before half-time and were unlucky not to find the breakthrough with 38 minutes played. Gassama drove forward with the ball as Rangers broke in numbers, before playing it out to Minsu on his right.
The South Korean’s shot was blocked by an Aberdeen defender, and with Shankland racing in towards the rebound at the back post, Afeez Aremu pulled off a fantastic clearance on the line to keep the game goalless.
From the resulting corner, Shankland saw a glancing header saved but Muller as the teams headed in level at the break.
Into the second-half, Aberdeen’s half-time substitute Stuart Armstrong dragged a low-left footed shot wide.
Muller pulled off a fantastic save with 56 minutes gone, as Minsu showed his quality from set-pieces sending a superb right-footed hit from a free kick towards goal with the Aberdeen goalkeeper getting enough on it to tip it over.
Rangers were awarded a penalty with 68 minutes played at Pittodrie as Djeidi Gassama picked up on a ball inside the box and tried to skip beyond Dan Happe, but the Aberdeen defender took him down with Matthew MacDermid pointing to the spot.
Lawrence Shankland stepped up to the spot, and it was a superb penalty from the skipper as he dispatched it high to the goalkeeper’s left hand side and ran off to celebrate in front of the travelling supporters.
With Gers in the lead, McInnes turned to his bench for the first time this afternoon with the introduction of Kosta Nedeljkovic and Daisuke Yokota in place of James Penrice and debutant Minsu.
The home side thought they were level with 82 minutes played, as their captain Kevin Nisbet found the back of the net. The ball was swung into the box by Stuart Armstrong, and Nisbet’s initial header was saved by Pandur, before Ayoub Mouloua headed off the bar, with Nisbet making no mistake in the rebound.
However, after a VAR check, the goal was disallowed for a push on Dujon Sterling from Nisbet at the initial header.
With five minutes added time at Pittodrie, Rangers saw out the match to secure the first league win of the season, with attention now turning to Falkirk on Wednesday.
RANGERS: Pandur, Sterling, Fernandez, Makhanya, Penrice (Nedeljkovic, 72), Neil, Devlin, Minsu (Yokota, 72), Curtis (Godfrey, 86), Gassama, Shankland (Naderi, 86)
Subs: Kelly, Barron, Chukwuani, Dragojevic, Aasgaard.
Aberdeen: Muller, Yogane (Armstrong, 46), Nisbet, Olusanya, Mayo, Guinness-Walker, Ronan (Mouloua, 75), Happe, Cadden, Ntelo (Smith, 63), Aremu.
Subs: Suman, Knoester, Briedl, Molloy, Milne, Fasanya.