Any notion that Steven Gerrard’s team will enjoy another serene procession in the title race was firmly rebuffed by a colossal effort from United at Tannadice.
Jamie Robson, one of many outstanding performers in tangerine, scored the game’s only goal in the 64th minute to spark joyous scenes among a home support who have been sceptical about Courts’ appointment.
The rookie head coach’s approval ratings will have soared on the back of a physically committed and tactically diligent display.
It all added up to a first league defeat in 17 months for Rangers who carried too many under-performing key players all over the pitch. There will be no repeat of the ‘invincible’ 2020-21 Premiership campaign for Gerrard.
Of more immediate concern to the Rangers manager will be his team’s struggles to hit their straps with the second leg of their Champions League third qualifying round tie against Malmo at Ibrox on Tuesday looming large.
While Rangers dominated possession against United, they were never able to exert any telling level of control on proceedings. They were hustled and harried to the point of distraction with midfielders Jeando Fuchs and Calum Butcher the disrupters-in-chief for the home side.
With the exception of Jon McLaughlin again replacing Allan McGregor in goal on league business, Gerrard fielded his strongest possible line-up which was testament to how tough he expected the assignment to be.
With Kemar Roofe unavailable because of a family issue, Alfredo Morelos was pitched straight back into action but the Colombian striker got little change all afternoon from a United defence superbly marshalled by Charlie Mulgrew.
With Ryan Kent having one of those days when nothing he tried came off, Joe Aribo looked the likeliest to make something happen for the visitors.
But they barely created any opportunities worthy of note - Morelos heading tamely straight at Benjamin Siegrist and James Tavernier forcing a smart save from the Swiss ‘keeper with a 25 yard shot - before Robson plundered the breakthrough for United.
Rangers had actually started the second half with better movement and sharper passing but they were caught out on the counter attack. John Lundstram failed to track back as United substitute Adrian Sporle linked up with Robson through the inside left channel.
United got a fortunate break of the ball off Steven Davis but there was nothing lucky about Robson’s fine finish as he got ahead of Connor Goldson to beat McLaughlin.
Goldson should have equalised in the 72nd minute, the big defender guilty of trying to be just too precise with a close range header from Tavernier’s corner.
Rangers laid siege to United’s goal in the closing stages and the sight of home players going down with cramp indicated the depth of their endeavour which eventually brought them all three points after five minutes of stoppage time.
Dundee United (4-3-3): Siegrist, Edwards, Mulgrew, Robson; Butcher, Fuchs, Harkes, Chalmers (Sporle 50), Clark, Pawlett (Watson 80). Subs not used: Carson, Reynolds, Neilson, Freeman, Mochrie.
Rangers (4-3-3): McLaughlin, Tavernier, Goldson, Helander, Barisic; Lundstram (Wright 69), Davis, Kamara; Aribo, Morelos (Defoe 82), Kent (Itten 79). Subs not used: McGregor, Patterson, Simpson, Arfield.