Ryan Naderi gave Gers the advantage from the penalty spot inside the opening 20 minutes, before a second-half strike from Dan Neil saw McInnes’ side sign off for the international break with three points.
There was one change from last weekend’s victory in the Premier Sports Cup semi-final against Aberdeen as Dan Neil came back into midfield to replace Tuur Rommens, with James Penrice dropping back into his more familiar left-back position.
Rangers started with Ivor Pandur in goal behind a back four of Dujon Sterling, Emmanuel Fernandez, Olwethu Makhanya and James Penrice.
Neil joined Raskin in midfield, while Minsu Kim and Badredine Bouanani took up position in the wide areas in support of strikers Kevin Kelsy and Ryan Naderi.
It was a lively start from Rangers, and Badredine Bouanani was first to have sight of goal as he sent a left-footed strike towards target after turning well to find space from a Dujon Sterling throw-in, but his effort was held by Jacob Chapman.
Ryan Naderi, who scored the winning goal last weekend, almost had the opener on 12 minutes as he got on the end of a flick on from Kelsy, but Chapman stood tall to block from close range.
From the resulting corner, Emmanuel Fernandez headed over a Minsu delivery as Gers looked for the early breakthrough.
With 16 minutes played, McInnes’ men were awarded a penalty after a foul on James Penrice inside the area. Minsu was driving forward another attack, before finding Penrice on the overlap. As he looked to get control of the ball, St Mirren midfielder Samuel Ramos caught the foot of the Gers full-back bringing him down with referee Nick Walsh pointing to the spot.
It was Ryan Naderi who stepped up, and the on-form striker rolled a right-footed penalty low to the goalkeepers left to give Gers a deserved lead.
There was a chance for St Mirren in the 37th minute as Ismeal Kabia intercepted a ball out from the back to create an opportunity for the home side. He found Jake Young in support, but his powerful strike was held well by Pandur.
It was Rangers who went in at the break with the advantage, but McInnes would be hoping his side could make it more comfortable in the second period, with the home side showing their threats in spells.
Badredine Bouanani fed through Minsu in the early stages after the break but it was blocked by Chapman.
There was a chance for the St Mirren side shortly after as a clearance from a cross broke for Killian Phillips and he sent a dangerous ball across the face of goal, with Jake Young looking to get a crucial touch but Pandur gathered.
At the other end Minsu played the ball forward into the path of Kevin Kelsy, but Chapman did enough to deny the striker from inside the box.
The second did come for Rangers on the hour mark and it was captain Dan Neil who found the back of the net. Kevin Kelsey looked to play forward to Minsu in a good move from Rangers, with the St Mirren clearance falling for Neil on the edge of the box and his strike was deflected beyond Chapman.
Ivor Pandur pulled off a great save at the other end to protect the two goal advantage, a cross into the box found St Mirren substitute Eseosa Sule, but the Gers number one was across well to deny the striker and push clear the danger.
Nico Raskin was denied by a good save at the other end, as he fired across goal from inside the box, but Chapman tipped it wide for a corner.
McInnes turned to his bench in the 74th minute with four changes as Findlay Curtis, Tuur Rommens, Djeidi Gassama and Tochi Chukwuani came on to replace Badredine Bouanani, James Penrice, Minsu and Kevin Kelsy.
Chukwuani flashed a shot just wide of target as he looked to make an instant impact in Paisley, before Curtis also had a good opportunity following a cut-back from Naderi but Chapman gathered.
There was a final change for Rangers with less than five minutes of the 90 remaining as Vanja Dragojevic replaced Dan Neil.
It was a good win on the road for Gers, with Motherwell away up next in the Scottish Premiership after the break.
RANGERS: Pandur, Sterling, Makhanya, Fernandez, Penrice (Rommens, 74), Raskin, Neil (Dragojevic, 87), Bouanani (Curtis, 74), Minsu (Gassama, 74), Naderi, Kelsy (Chukwuani, 74).
Subs: Kelly, Nedeljkovic, Godfrey, Miovski.
St Mirren: Chapman, John, Jackson, Ramos (Thomas, 64), Gogic (Douglas, 86), Kabia, Young (Sule, 64), Fraser, Taylor (Donnelly, 64), Ramsay, Phillips.
Sub:Tamosevicius, Richardson, Fieldson, McEvoy, Mochrie.
