Goals from Tomi Horvat and Otar Kiteishvili gave the home side the advantage at half-time before Djeidi Gassama responded for Rangers in the second-half. Despite an improved second-half display, Gers were unable to add to that as the Austrian side took all three points.
There was one change from the team which defeated Livingston on Sunday as Youssef Chermiti came in to replace Bojan Miovski in attack. That meant Rangers lined-up with Jack Butland in goal behind a back four of James Tavernier, John Souttar, Derek Cornelius and Jayden Meghoma.
Nico Raskin, Connor Barron and Thelo Aasgaard were in midfield, while Djeidi Gassama and Oliver Antman provided the support for Chermiti.
It was not the start Gers were looking for in Austria as the home side took the lead with only seven minutes played. A Rangers throw-in was intercepted by Dimitri Lavalée who found Maurice Malone ahead of him and he was able to cut it back to Tomi Horvat. The midfielder took a touch inside the box before sending a shot into the back of the net.
Jack Butland pulled off a big save shortly after, as Otar Kiteishvili played a pass through to Belmin Beganović who had made a good run into the box, but the Rangers number one matched his effort with a block.
The first big chance for Rangers came with 14 minutes played as Djeidi Gassama did well down the left to beat the defender and whip an inviting delivery into the box which Youseff Chermiti got his head to, but the striker was denied a first Rangers goal by the woodwork.
Nico Raskin headed over shortly after as Gers searched for an equaliser in this tie, before Butland pulled off another fantastic stop to keep it 1-0. A Strum Graz throw-in came in from the right-hand side, with Horvat and Malone combining before the latter released a powerful strike towards goal but Butland was strong to block the effort.
The chances were there for Rangers too, with Antman finding Chermiti just after the hour mark and the striker got his right-foot to the ball inside the box as he tried to lift it over the keeper but Christensen was positioned well to hold it.
However, with 35 minutes played in Graz, the home side were able to double their lead from a free-kick. Horvat was the provider this time as he rolled a low free-kick towards goal, which beat the Rangers defence and set up Otar Kiteishvili to touch beyond Butland.
Martin turned to his bench at half-time with two changes as Rangers looked for a route back into the match. Max Aarons replaced Jayden Meghoma, which saw Derek Cornelius shuffled into the left back position, with James Tavernier and John Souttar at centre-back and Aarons slotting in on the right of the defensive line.
The other change saw Oliver Antman replaced by Bojan Miovski as he joined Youssef Chermiti in attack.
It didn’t take long for Rangers to have that goal they needed to start the second-half. Jack Butland played it into Nico Raskin in the middle of the pitch, and the midfielder sent the ball out the left to Djeidi Gassama.
The winger showed his skill as he cut inside and sent a lovely finish into the back of the net for his fifth goal of the season.
Joe Rothwell was next to be introduced for Rangers, as he came on to replace Connor Barron for the final 25 minutes.
A free-kick opened up another opportunity as James Tavernier lifted the ball into the box and Nico Raskin headed towards the back post, but the defender did just enough to touch it out of the way of Miovski and Chermiti.
Rangers were pushing for an equaliser, and Derek Cornelius was denied by a fantastic one handed save from the goalkeeper before the ball was returned to the area by Thelo Aasgaard with John Souttar sending it back goalwards, but Christensen was once again able to do enough to push away the header.
Graz substitute Leon Grgic had a chance at goal as the home side broke up the pitch, but his low strike was held by Butland as he got down to his right to gather.
A final change followed for Rangers as they continued to search for the equaliser with Danilo coming on for Thelo Aasgaard.
There was another big save from Christensen in the 89th minute as he tipped over a Danilo strike from close range but it was the final opportunity as the home side secured the points.
RANGERS: Butland, Tavernier, Souttar, Cornelius (Moore, 78), Meghoma (Aarons, 46), Raskin, Barron (Rothwell, 68), Aasgaard (Danilo, 83), Gassama, Antman (Miovski, 46), Chermiti.
Subs: Kelly, Wright, Cameron, Djiga, Danilo, Rice, Curtis, McCallion
Sturm Graz: Christensen, Stanković, Oermann (Mitchell, 73), Kiteishvili (Grgic, 73), Karic, Horvat (Geyrhofer, 83), Chukwuani, Lavalée, Beganović (Hödl, 60), Aiwu, Malone (Jatta, 73).
Subs: Wiener-Pucher, Bignetti, Black, Hierländer, Haider, Weinhandl.