Samuel Cleall-Harding opened the scoring for the visitors on 20 minutes, the centre-half glancing a header into the net from a well-taken corner-kick.
The Light Blues, however, responded swiftly and in impressive style, with Dessers producing a stunning header from a brilliant Jefte cross just five minutes later.
Dessers put his side back in front on 73 minutes from the penalty spot, taking his tally of goals for Rangers to 50, before man of the match Nico Raskin quickly made it three with an accurate finish from Vaclav Cerny’s assist.
Head coach Barry Ferguson made two changes to his starting line-up following Sunday’s 4-0 victory over Aberdeen, with number one Jack Butland replacing Liam Kelly between the posts and Hamza Igamane in for Nedim Bajrami.
With the sun shining down on the SPFL Pitch of the Season, Raskin got the action underway from the kick-off with Rangers shooting towards the Broomloan Road Stand in the first half.
And the Light Blues certainly started the 90 minutes in a positive manner, retaining possession and forcing the visitors to sit deep in their own half and soak up the early pressure.
On nine minutes, a short pass from Mohamed Diomande to Jefte resulted in the Brazilian being floored by a clumsy challenge from Kai Fotheringham. Referee Calum Scott was close to the tackle but kept his cards in his pocket to the surprise of the Ibrox faithful.
Rangers then produced the first goalscoring opportunity of note when captain James Tavernier’s teasing, deep cross dropped to Igamane but his header went back across goal and wide of the far post.
United responded with a good passage of play with the ball falling in the box to former Gers winger Glenn Middleton. His low, drilled shot from 16 yards was confidently held by Butland.
The game was now opening up with both teams looking to break the deadlock. Next up to try his luck was Dessers who, with his back to goal, showed quick feet to turn just inside the box but his effort was easily gathered by United goalkeeper David Richards.
On 19 minutes, the Tangerines pushed forward with intent and when Fotheringham forced the ball through to striker Sam Dalby the opening goal was the expected outcome. Butland, at full stretch, got down brilliantly to get his fingertips to the ball.
From the resulting corner, however, United got their noses in front and it was all too easy for them. Ryan Strain’s near-post delivery was met by the unmarked Cleall-Harding, who glanced the ball past Butland to give his side the lead.
The Taysiders one-goal advantage didn’t last long – just five minutes - as Rangers bounced back quickly from going behind, with Dessers scoring a terrific equaliser.
Jefte’s impressive delivery from the left flank was perfect for his teammate who directed a sweet header into the postage stamp corner of the net.
With Ferguson urging his players to keep pushing forward and half-time approaching, Cerny tried his luck with a trademark shot from distance which went straight into Richards’ hands.
With 43 minutes on the clock, Diomande then let fly from 20 yards but the ball flew past the post, meaning the first half finished 1-1.
With no substitutions made at the interval, Rangers started the second half in control but chances were few and far between before the hour mark.
Their opportunity to take the lead arrived with 17 minutes remaining when Vicko Sevelj, who had earlier been booked, clattered into Diomande in the box and the referee, after checking the VAR monitor, pointed to the penalty spot.
Regular taker Tavernier allowed Dessers to step up and he made no mistake from 12 yards, sending the keeper the wrong way for his 50th Rangers goal.
If that was a sweet moment for the players and fans to enjoy, the third goal for Ferguson’s side on 75 minutes was the icing on the cake.
Cerny picked up the ball on the right wing and he waited for the right moment to play a perfect pass to Raskin ahead of him.
The Belgian took aim and fired a terrific finish into the roof of the net to secure all three points for his team and send the Ibrox faithful home happy for the last time this season.
RANGERS: Butland, Tavernier, Souttar, Balogun, Jefte (Kasanwirjo 73), Barron (Rice 82), Diomande (Lawrence 73), Raskin, Cerny (Cortes 80), Igamane (Danilo 80), Dessers.
Subs not used: Kelly, Propper, Bajrami, Curtis.
Goals: Dessers 25, 73pen, Raskin 75
DUNDEE UNITED: Richards, Strain, Cleall-Harding, Gallagher, Ferry, Sevelj (Paton 88), Campbell, Docherty (Babunski 80), Middleton (Trapanovski 80), Dalby (Van der Sande 81), Fotheringham.
Subs not used: Walton, Moult.
Goals: Cleall-Harding 20
Bookings: Sevelj