Ryan Naderi came up with the crucial second-half goal, before Cammy Devlin saw red for Gers in the first-leg at Ibrox.
There was one change from the weekend victory over St Mirren as Dan Neil came in to replace Nico Raskin, with McInnes confirming pre-match the Belgian had been suffering with an ankle problem.
That meant Rangers lined-up with Ivor Pandur in goal, behind a back four of Dujon Sterling, Emmanuel Fernandez, Olwethu Makhanya and James Penrice.
Neil joined Vanja Dragojevic and Tochi Chukwuani in midfield, while Daisuke Yokota and Djeidi Gassama provided the support for Ryan Naderi.
There was a place on the bench for lasted signing Kosta Nedeljković, and he was joined there by Liam Kelly, Ross McCrorie, Cammy Devlin, Nico Raskin, Connor Barron, Lyall Cameron, Ross McCausland, Findlay Curtis, Thelo Aasgaard, Bojan Miovski and Lawrence Shankland.
The Czech side had progressed through two qualifying rounds prior to reaching the play-off stage, with this evening’s match the first competitive meeting between the two sides.
Inside the opening 10 minutes, Gassama tested the goalkeeper with a powerful strike from distance which Jan Hanuš pushed over the bar. Dragojević, who scored a spectacular first Rangers goal at the weekend, almost found the target again from outside the area but it bounced wide of the keeper’s right-hand post.
Rangers were really pushing for the opening goal, and in the space of 30 seconds, James Penrice had a shot saved by the goalkeeper, before Dragojević hit the post in a good spell of pressure from McInnes’ men.
Early in the second-half, there were calls for a penalty around Ibrox as Yokota nicked the ball from a Czech defender in a dangerous area to play in Ryan Naderi. The striker collided with Jablonec captain Nemanja Tekijaški inside the area but after a VAR check play continued.
However, in the 50th minute, Rangers had the lead and it was Naderi who found the back of the net with his second goal in two games. It was a good delivery into the area from Dan Neil as he searched for Yokota at the back post, and the winger did enough to head back into the path of Naderi, who finished from close range.
There was a fantastic chance for a second as Naderi this time turned provider with a delivery from the right, but Gassama was unable to keep his effort down.
McInnes made his first changes with just over 20 minutes remaining as Findlay Curtis and Cammy Devlin came on to replace Daisuke Yokota and Vanja Dragojević.
Devlin was instantly involved with a tackle on Jiří Sláma which was later reviewed by VAR and the midfielder was shown a straight red card.
After the sending off, the visitors enjoyed a spell of possession, with a header from Martin Cedidla held by Ivor Pandur.
A double change followed for Rangers as Nedeljković came on for his Rangers debut alongside Connor Barron, with Dan Neil and Djeidi Gassama going off.
With four minutes added at Ibrox, Gers were still on the hunt for a second goal to extend their lead, as Lawrence Shankland was introduced for goalscorer Naderi.
Rangers were unable to carve out another opportunity in injury time, and will head to Jablonec with a one goal lead next week in a bid for a place in the UEFA Conference League league phase.
Rangers: Pandur, Sterling, Fernandez, Makhanya, Penrice, Neil (Barron, 86), Dragojević (Devlin, 69), Chukwuani, Yokota (Curtis, 69), Gassama (Nedeljković, 86), Naderi (Shankland, 90).
Subs: Kelly, McCrorie, Raskin, Cameron, McCausland, Aasgaard, Miovski.
FK Jablonec: Hanuš, Tekijaški, Tchanturishvili, Suchan (Zorvan, 62), Sedláček, Pavlovic, Cedidla, Sláma (Růsek, 81) , Polidar (Ahl, 62), Nebyla (Chramosta, 81), Jawo
Subs: Mihelak, Růsek, Souček,, Sobol, Vecheta, Novák.