Philippe Clement’s men were unable to find a breakthrough they needed despite chances at Dens Park.
The manager named three changes from the weekend’s defeat to Ross County as Kemar Roofe came in for his first league start since December, with Dujon Sterling and Tom Lawrence also named in the starting XI.
That meant Rangers started at Dens Park with Butland in goal behind a back four of James Tavernier, Connor Goldson, John Souttar and Dujon Sterling.
John Lundstram, Tom Lawrence and Todd Cantwell made up the midfield three, while Roofe came into attack alongside Fabio Silva and Abdallah Sima.
It was Rangers who got the action underway at Dundee as they looked to respond from the weekend’s defeat to Ross County.
The home side were first to threaten at goal with less than a minute on the clock as the ball fell for Malachi Boateng just inside the box and he released a right-footed shot across goal which was just inches wide of the post.
At the other end, James Tavernier lifted the ball into the box in search of Kemar Roofe at the back post but his header was unable to trouble McCracken in the Dundee goal as it drifted just wide.
The hosts were forced into an early change as captain Joe Shaughnessy went down in the middle of the pitch and had to be replaced by Antonio Portales.
McCracken pulled off an impressive save with just over 10 minutes played as Rangers looked to take an early lead in this game. Todd Cantwell found the run of Abdallah Sima with a lovely pass and the winger used his pace to take a touch and create space before striking the ball towards goal but the Dundee stopper did well to block the effort.
Sima again was denied by McCracken as the on-loan Brighton forward continued to create problems for the home side in these opening stages.
It was a fairly even opening period in this game, with Butland forced into a save as he got down low to his left to push wide a volley from Jordan McGhee.
With just over 20 minutes played at Dens, the home side thought they had found the breakthrough as Luke McCowan’s free-kick was tapped home on the rebound after a double save from Butland but the referee’s flag was raised for offside and, fortunately for Rangers, the goal was disallowed.
Rangers were next to threaten from a set-piece, and it was the captain who tested McCracken as he looked to curl a free-kick into the back of the net but it was pushed wide by the Dundee goalkeeper.
From the resulting corner, defender Connor Goldson sent Tavernier’s delivery goalwards but McCracken was again on hand to deny Rangers.
In the final seconds of the first-half, Tom Lawrence weaved his way into the box before getting a shot away at goal, but he was unable to keep the strike down as it drifted over the bar as the teams headed in at the break goalless.
With less than 10 minutes of the second-half played, Clement turned to his bench as Rangers continued to look for the opening goal in this match. It was a triple change as Cyriel Dessers, Kieran Dowell and Rabbi Matondo replaced Kemar Roofe, Todd Cantwell and Fabio Silva.
Tom Lawrence had a low drilled shot blocked as Dundee continued to hold strong at Dens.
With 72 minutes of the game played, Rangers had their best chance of the half so far as Connor Goldson found Kieran Dowell in space in the middle of the pitch and he found the run of Cyriel Dessers.
The striker did well to take a touch in the box and looked to guide a shot into the top of the net, but it was pushed wide by McCracken. There was another change for Rangers for the final 10 minutes as Ross McCausland was introduced in place of Abdallah Sima.
Matondo tried a shot from distance as he again cut in from the left to send a strike towards goal, but it was wide of the target from the Welshman. With a few minutes of the game remaining, Rangers were awarded a free-kick but it was curled just over the bar by James Tavernier.
RANGERS: Butland, Tavernier, Goldson, Souttar, Sterling, Lundstram, Lawrence, Cantwell (Dowell, 56), Silva (Matondo, 56), Sima (McCausland, 79), Roofe (Dessers, 56).
Subs: McCrorie, Davies, Barisic, King, Raskin.
Dundee: McCracken, Dodgson, Shaughnessy (Portales, 10), McGhee, Tiffoney (Costelloe, 63), Bakayoko (Main, 63), Cameron, Lamie, McCowan, Boateng, Sylla.
Subs: Carson, Astley, Mulligan, Robertson, Donnelly, Mellon.