Oluwaseun Adewumi gave the home side the lead early in the match, before Cerny drew Rangers level before half-time.
From the weekend’s 3-3 draw with Hibs, Clement made two changes to his starting line-up. Clinton Nsiala came in for his first competitive start in place of the injured Dujon Sterling while Connor Barron replaced Nico Raskin, who was suspended.
With captain James Tavernier and vice captain Jack Butland both out injured, Robin Propper wore the armband this evening.
Rangers lined-up with Liam Kelly in goal behind a back four of Ridvan, Robin Propper, Clinton Nsiala and Jefte. Connor Barron was in midfield alongside Mohamed Diomande and Nedim Bajrami, while it was the same front three with Vaclav Cerny and Ianis Hagi supporting Hamza Igamane.
Nedim Bajrami had the first chance for Rangers as he fired a ball over the target with just three minutes on the clock as the visitors looked for a quick start at Dens Park.
However, with only six minutes played it was Dundee who took the lead. An initial shot from Scott Tiffoney was blocked by the Rangers defence but Josh Mulligan was quickest to react at the byline and managed to deliver a cross back into the danger area, with Oluwaseun Adewum sending the ball beyond Liam Kelly.
Aaron Donnelly saw a header deflected wide from a Dundee corner as they looked to take advantage of a period of pressure, before Ridvan tried a shot from the edge of the box at the other end but it was just over the bar from the full-back.
Rangers were level with 34 minutes played in a quick counter-attacking move from Clement’s men. Liam Kelly played it out to Ianis Hagi on the left and he found Hamza Igamane who fed the ball to Vaclav Cerny who had cut inside from the right.
The winger did well to send a composed finish beyond Carson for his 11th goal of the season, and to draw Rangers level in this match.
Philippe Clement made a change to his side at half-time as Ianis Hagi was replaced by Rabbi Matondo for the second-half in Dundee.
Trevor Carson came up with a big save early in the second-half as a good cross from Jefte evaded the Dundee defence with Vaclav Cerny sending a powerful left-footed shot towards goal but it was blocked by the goalkeeper, with Cerny unable to find the target with the rebound as it drifted over the bar.
Oluwaseun Adewumi had the ball in the net again for Dundee as he tapped home a Simon Murray cross, but it was disallowed for offside after a VAR check.
Clement turned to his bench again with 66 minutes played as Danilo came on to replace Connor Barron.
Hamza Igamane forced a save from Carson with a powerful right-footed strike from a central area on the edge of the box but the Dundee goalkeeper matched the effort with a good block.
Dundee were still looking threatening too as Vetro delivered a ball into the box in search of Adewumi, but he was unable to keep it down as it went high of the bar.
Another chance came for the home side with 15 minutes remaining as Adewumi nicked the ball from Jefte around the half-way line and launched another attack, getting a shot away himself which was blocked by Kelly.
Ross McCausland replaced Ridvan for the final 10 minutes as Rangers continued to look for a winning goal in Dundee.
Rangers were getting closer to that all important second goal, as Mohamed Diomande hit the crossbar with a looping strike as the match approached the final few minutes.
There were four minutes added on at Dens Park, but the Light Blues were unable to carve out another opportunity as they left Dundee with a point.
RANGERS: Kelly, Ridvan (McCausland, 81), Propper, Nsiala, Jefte, Barron (Danilo, 66) Diomande, Cerny (Cortes, 87), Bajrami, Hagi (Matondo, 46), Igamane.
Subs: Munn, Dessers, Dowell, King, Rice.
Dundee: Carson, Ingram, Robertson, Astley, Tiffoney (Vetro, 70), Mulligan, Adewumi, Garza (Braybrooke, 78), Murray (Palmer-Houlden, 70), Sylla, Donnelly.