A Lewis Mansell strike was diverted into the net after taking a deflection on the 85th minute before Alex Jones got the second with just three minutes remaining.
Rangers fielded a side mixed with youth and first-team players as Matt Polster, Jake Hastie and Brandon Barker came into Graeme Murty’s starting eleven.
Kai Kennedy had an early shot for Rangers with just three minutes on the clock as Dapo Mebude diverted Jake Hastie’s cross into his path but the shot was just wide from the number 10.
Kennedy again threatened the Partick Thistle goal just a few minutes later as he swung a dangerous free-kick into the area, which troubled goalkeeper Jamie Sneddon who was dealing with low sun, but the free-kick was turned behind for a corner.
In a spell of early pressure from the Gers Brandon Barker saw his shot from inside the area blocked by Sneddon.
Partick had their first effort of the game on the 13th minute as Alex Jones’ shot had Keiran Wright at full stretch as it drifted just wide of the Rangers goal.
Jones took a free-kick on the 24th minute as he tried to curl the ball into the top corner from the edge of the box but it was just over the bar.
Matt Polster had a good chance for Rangers a few minutes later as he got on the end of a Jake Hastie corner but his effort was glanced just wide of the target.
Early in the second-half Jamie Barjonas tested the keeper as his powerful strike from 25-yards was tipped over by the Thistle keeper.
At the other end Kieran Wright was called into action as he produced a good save to deny Rangers’ loanee Cammy Palmer from opening the scoring for Partick Thistle.
Wright produced another save just after the hour mark as he pushed wide a shot from Thistle substitute Joe Cardle.
Rangers were pressuring late on for a goal with Kai Kennedy sending a cross into Dapo Mebude but he couldn’t get enough of a touch on the ball and it was saved by Jamie Sneddon.
The Partick Thistle keeper had a great double save as he denied Lewis Mayo from close range before Dapo Mebude cut in from the right to fire his shot just wide.
Gary Caldwell’s side opened the scoring on the 85th minute as Lewis Mansell’s shot was turned into the net after taking a deflection off of a Rangers defender.
The Championship side got their second just two minutes later as Alex Jones doubled the scoring.
Rangers: Wright, Patterson, Maxwell, Mayo, Breen, Polster, Hastie (Young-Coombes,87), Barjonas, Mebude, Kennedy, Barker (Atakayi, 67). Subs: Budinauckas, Finlayson, Thomson, Balde, Butterworth.
Partick Thistle: Sneddon, Renfrew (Bannigan, 58), Robson, O’Ware, Trailist, Palmer, Galasso (Cardle, 58), Niang (Mansell, 65), Jones, Gordon, De Vita (Saunders, 65). Subs: Fox, Cardle, Sauders, Mansell, Rodden, McIntyre, Bannigan.