Philippe Clement's men were under pressure to respond after blowing five points in the past week to hand Celtic the advantage in the Scottish Premiership title race.
"It's a very important thing because we had two knocks this week," said Clement.
"We are in a title chase, we are in a cup final, and we are really hungry for more trophies. I think everyone in Scotland will be really excited about that, that there's a challenge for trophies."
Dessers was one of those in the firing line for his inconsistent form, but took his tally for the season to 19. The Nigerian settled Rangers' nerves with a cool finish after just five minutes.
However, victory came a cost for the Gers as on-loan Brighton forward Abdallah Sima limped off with what looked like the recurrence of a hamstring injury.
Rangers needed to rely on goalkeeper Jack Butland to make terrific saves from Alan Forrest and Frankie Kent in quick succession to remain in front at half-time.
However, they made the game safe 12 minutes from time to remain in contention for a domestic treble. Dessers again applied the finishing touch after his first effort was saved by Craig Gordon.
Celtic, meanwhile, needed an epic penalty shootout to see off Aberdeen on Saturday after a thrilling 3-3 draw. The Glasgow giants will face off in the final on May 25.
