Having watched Thursday’s 3-2 triumph against Arsenal from the stands, the 63-year-old interim manager was on the Old Trafford touchline for the first time when Patrick Vieira’s men came to town.
Rangnick’s reign – and first match as a manager in 925 days – began in victorious fashion on Sunday, when Fred proved the unlikely match-winner with a superb curling late effort that saw off Palace 1-0.
United’s third Premier League win in 10 matches also brought with it a first home clean sheet of the campaign on an afternoon when a superb start petered out, providing the German with plenty of food for thought.
The hosts began with impressive intensity and energy under their new boss, with Cristiano Ronaldo having a host of chances before their performance began to drift against hard-working Palace.
Alex Telles saw a free-kick skim the bar and Jordan Ayew went agonisingly close at the other end as United began to slip into familiar ways, only for Fred to produce a moment of magic to seal three points.
Rangnick stood in the technical area for the majority of his first match in charge. The German kept with the side that beat Arsenal but favoured a 4-2-2-2 formation as players pressed with more regularity and effectiveness.
That tweak, and the chance to impress Rangnick, saw the hosts start strongly, with Telles flashing an early shot wide before a Ronaldo cross-shot just evaded Bruno Fernandes.
David De Gea held onto a Wilfried Zaha snapshot on a rare Palace voyage forwards, before Ronaldo fired a free-kick over and then saw Marc Guehi recover well to get in a block on him after being found by Fernandes.
The 36-year-old star powered over a header from just inside the box and stung Vicente Guaita’s palms as United continued on the front foot.
James Tomkins blocked a goalbound Fred drive as sustained pressure continued.
Guaita stretched to tip away a low Fernandes effort, before Palace survived some penalty box pinball and a deflected Jadon Sancho effort looped just over.
But a break in play for treatment after Nathaniel Clyne’s foul on Fred allowed Palace to gather their thoughts and gain more control.
Ayew’s hopeful curling effort skipped just wide as the Eagles frustrated a United side that had settled into old patterns towards the end of the first half.
However, they had a big change in stoppage time as dogged play and good link up with Scott McTominay ended with Diogo Dalot flashing just across the face of goal.
It was an encouraging first half followed by a more cumbersome second period by United.
Cheikhou Kouyate saw a header blocked from a threatening set-piece from Conor Gallagher, who helped close down Marcus Rashford as the forward shaped to shoot.
Mason Greenwood replaced Sancho in a bid to inject new life into a performance that had become flat and somewhat sloppy.
An audacious free-kick nearly provided a 68th-minute opener. Guehi was booked for bringing down Rashford and Telles clipped the top of the crossbar from the resulting set-piece, which he hit well from an acute angle.
Greenwood swiped wide and Rangnick turned to Anthony Elanga to aid a performance that was now a far cry from the start of proceedings, with Palace going agonisingly close to breaking the deadlock in the 75th minute.
Tomkins headed a fine corner to the far post, where Ayew could only direct across the face of goal from an acute angle.
It was a let-off punished in style two minutes later as Greenwood laid back to Fred, who curled a superb 20-yard effort beyond Guaita in front of the Stretford End.
The goal was met with a mixture of relief and joy by the Old Trafford faithful, who soon sung former manager Ole Gunnar Solskjaer’s name as well as that of ex-caretaker boss Michael Carrick.
Harry Maguire had to be bandaged up after a clash of heads and De Gea had to tip a threatening cross behind as Rangnick started his reign with victory.