Ryan Naderi scored a double either side of a Kevin Kelsy strike, to give Gers a 3-0 lead at half-time, before Kilmarnock got one back in the final minutes of the match.
McInnes named the same team as the last Scottish Premiership outing in the Old Firm as he looked for his side to pick-up where they left off last month.
Rangers started with Ivor Pandur in goal, behind a back line of Dujon Sterling, Emmanuel Fernandez, Olwethu Makhanya and James Penrice.
Dan Neil captained the team in midfield alongside Nico Raskin, while Djeidi Gassama and Minsu Kim supported strikers Ryan Naderi and Kevin Kelsy.
It was Neil who got the action underway, and in the opening 15 minutes, Rangers were dominating possession and, with their first real chance, got the opening goal.
James Penrice sent a perfect cross into the box from the left, with Ryan Naderi beating his defender to send a glancing header into the back of the net for his fifth goal of the season.
Minsu tested Kilmarnock goalkeeper Calum Ferrie shortly after as Emmanuel Fernandez found the winger in space and he got a shot away, but it was held by Ferrie.
The second goal did come shortly after as McInnes’ men doubled their advantage inside 25 minutes. Dan Neil closed down a Kilmarnock player in the middle of the pitch, and came away with the ball, before sending it into the box in search of Kevin Kelsy.
The striker did well to control it onto his left foot, before directing a shot towards the goal which beat the goalkeeper for his first Scottish Premiership goal for the club.
It was a brilliant start from Rangers who looked threatening, and Gassama was next to have an effort as Minsu drove down the right before cutting it back, but his strike was cleared by MJ Kamara.
Joe Hugill fired a powerful hit over the bar as Kilmarnock searched for a route back into this one, before Erik Ring curled a left-footed shot over the bar in a spell for the visitors.
However, it was three for Rangers before the break, and another for Ryan Naderi. It again came down the left with Gassama and Penrice combining before the former sent a shot towards goal and Naderi got the final flick to turn it into the back of the net.
There was a change for Rangers at the break, as Kosta Nedeljkovic came on to replace Dujon Sterling.
Kilmarnock thought they had a goal back with 57 minutes on the clock as Tyreece John-Jules turned and sent a low strike beyond Pandur, but the flag was up for offside.
Ivor Pandur pulled off a fantastic save shortly after as he tipped over a shot from Aaron Tshibola.
McInnes turned to his bench again with 20 minutes remaining at Ibrox, as Findlay Curtis was introduced to replace Kevin Kelsy.
Gassama sent a shot high over the bar, before Minsu had a shot deflected wide from inside the box.
Badredine Bouanani, Bojan Miovski and Tochi Chukwuani came on for Djeidi Gassama, Minsu and Dan Neil for the final few minutes at Ibrox.
Kilmarnock had a goal back in the 89th minute as they broke two v one up the pitch, with Nicky Clescenco finishing beyond Pandur.
RANGERS: Pandur, Sterling (Nedeljkovic, 45), Fernandez, Makhanya, Penrice, Neil (Chukwuani, 87), Raskin, Minsu (Miovski, 87), Gassama (Bouanani, 87), Kelsy (Curtis, 73), Naderi.
Subs: Kelly, Godfrey, Rommens, Dragojevic.
Kilmarnock: Ferrie, Kamara (Brandon, 79), McCarthy, Ring (Clescenco, 75), Hugill, John-Jules, Kiltie (Daniels, 79), Stanger, Lowery, Schjonning-Larsen, Tshibola.
Subs: Armour, O’Hara, Deas, McKenzie, Meier, Owen.
