McInnes’ men secured another three points in the league, with Shankland’s goals coming either side of an own goal to secure the victory at the Falkirk Stadium.
There were two changes from the weekend’s win over Aberdeen as Nico Raskin and Kosta Nedeljkovic came in from the start, with Dujon Sterling and Dan Neil out of the squad.
Rangers lined-up with Ivor Pandur in goal behind a back four of Nedeljkovic, Emmanuel Fernandez, Olwethu Makhanya and James Penrice.
Nico Raskin returned alongside Cammy Devlin in midfield, while Findlay Curtis, Minsu and Djeidi Gassama provided the support for Lawrence Shankland.
Manager Derek McInnes was in the stands this evening, serving the first match of a two-match touchline ban, and was looking for his team to build on Sunday’s victory at Pittodrie.
It was the perfect start as with only eight minutes played Shankland fired Rangers ahead. It was a nice move as James Penrice raced forward before finding Gassama on the left. The winger sent a ball into the box, with Shankland taking a touch onto his left foot before sending a looping strike over the goalkeeper.
Minsu came close to doubling the advantage inside the opening 20 minutes as his right-footed strike came back off the post.
At the other end, Liam Henderson released an effort from distance towards goal, but it was gathered well by Ivor Pandur.
It was a good opening period from Rangers, and Minsu was again looking lively as he carved open space for a right footed shot which was pushed away by Scott Bain with Raskin only able to turn the rebound into the side netting.
With 10 minutes to go in the first-half, Minsu played a nice ball forward to Findlay Curtis, but his shot from a tight angle was pushed away by Bain.
However, Falkirk had their equaliser before half-time as Ethan Ross’ cross was turned into his own net by Kosta Nedeljkovic.
Into the second-half, there was a good chance for Falkirk as Ethan Ross cut the ball across the face of goal to Jacob Murrell but his close-range shot was held by Pandur.
Almost immediately, Rangers broke up the other end, with Curtis laying the ball to Shankland, but his sweeping shot was just wide of the target.
There was a double change for Gers as the game approached the hour mark. Ross McCrorie came on to replace Kosta Nedeljkovic at right-back, while Cammy Devlin made way for Tochi Chukwuani in midfield.
Pandur was called into action to tip over a header from Jacob Murrell as both teams continued to search for another goal in this match.
Murrell had another chance minutes later as he intercepted an Emmanuel Fernandez pass to have a clear opening at goal, but Ivor Pandur was able to push away the shot.
Gassama was next to have a chance at goal as he cut inside from the left and looked to place a low shot beyond Bain, but it bounced just wide of the post.
Rangers had the lead, and it was Shankland again with his second goal of the evening. McCrorie did well to take the ball round Falkirk bodies on the edge of the box, before Shankland turned to place a low shot beyond Bain.
Further changes followed for Gers with Bojan Miovski and Daisuke Yokota replacing Findlay Curtis and Minsu for the final 10 minutes.
Rangers were comfortable in the closing stages as the secured another three points in the Scottish Premiership.
RANGERS: Pandur, Nedeljkovic (McCrorie, 58) Fernandez, Makhanya, Penrice, Raskin, Devlin (Chukwuani, 58), Curtis (Yokota, 79), Minsu (Miovski, 79) , Gassama, Shankland (Godfrey, 91). Subs: Kelly, Dragojevic, McCausland, Naderi. Falkirk: Bain, McCann, Henderson, Spencer (Melniks, 77), Neilson, Barbrook, Strain, Ross (Parkinson, 77), Murrell (MacIver, 69), Krauhaus, Fodrey (Doherty, 53).
Subs: Hogarth, McMillan, Donaldson, Tanser, Allan.