Nahki Wells ended up on the losing side on his full Huddersfield Town debut after a Charlie Austin double for Rangers.
Rangers, heavily dependent on Austin this season, struggled before their top scorer opened the scoring by finishing emphatically on 55 minutes after Clint Hill’s lofted ball forward had been flicked on by Niko Kranjcar and then Andy Johnson.
The Terriers were impressive and looked set to secure a deserved point when recent signing Wells levelled midway through the second half, heading home a cross from Adam Hammill.
But striker Austin’s header with 12 minutes remaining from Benoit Assou-Ekotto’s right-wing corner proved decisive.
Huddersfield boss Mark Robins admitted the defeat was tough to take.
He said: “On the one hand we played really well but on the other we’ve not got that point, so it’s difficult to swallow.
“In the first half I thought we were brilliant. That’s no surprise to me, because we’re good. We came here and took the game to them.
“We’ve done well, but we had clear-cut chances and should really have been 3-0 up at half- time. We didn’t take those chances and you know they are then going to come at you in the second half.
“We conceded a poor goal from a defensive point of view and then they got the winner from a set-play after we had clawed our way back in with the goal from Nahki.
“To make that next step we’ve got to play like we did in the first half for the whole of the game. But I still thought we were good value for at least a point.”