Heckingbottom's future had come under intense scrutiny in the immediate aftermath of the heavy loss at Turf Moor, which came against a Burnley side that went into the match sitting bottom of the table and without a home league win all season.
The club has now confirmed that Heckingbottom has been relieved of his duties, ending his two-year reign at Bramall Lane, and ended that statement by saying that they hope to have a new manager in place before Wednesday's Premier League meeting with Liverpool.
Less than 20 minutes later, the Blades announced the return of Wilder on an 18-month contract, reappointing the 56-year-old less than three years after originally sacking him in March 2021.
"Firstly, on behalf of the board of directors, I'd like to thank Paul for all of his efforts at Sheffield United, firstly as U23s manager before stepping up to take control of first-team duties," read a statement from Sheffield United CEO Stephen Bettis.
"His professionalism and dedication have been a credit to the club and I'm sure all Unitedites enjoyed the promotion-winning campaign.
"However, after slipping to the bottom of the table and a number of disappointing results and performances, it is felt that a change is needed to give the club a boost and every possible chance of remaining in the Premier League beyond this season."
The former Barnsley, Leeds United and Hibernian boss won exactly half of his matches in charge of the Blades, picking up 49 victories, 18 draws and 31 defeats in 98 games.
Sheffield United earned promotion to the Premier League under Heckingbottom last season, but have since won just one league game all term, losing 11.
Among the more notable defeats this season have been an 8-0 loss at home to Newcastle United and 5-0 hammerings at the hands of Arsenal and Burnley, while they were also knocked out of the EFL Cup by Lincoln City.
Sheffield United not only have the lowest points tally in the Premier League this season, but they have also scored the fewest goals, registered the fewest amount of shots, conceded the most goals and allowed more shots against them than any other team.
Wilder previously spent almost five years as Sheffield United manager from 2016 to 2021, taking the club from League One to the Premier League and winning 106 of his 227 matches at the helm.
A former player for the Blades as well, Wilder has since spent time in charge of Middlesbrough and Watford, but has been out of work since leaving the Hornets in the summer.
Confirming Wilder's return, Bettis said: "Following discussions, the board feel that Chris Wilder is the best possible option to give the Blades a change in fortune at this time and everyone at the club is delighted to welcome him back.
"His love for United and desire to improve the current situation is undeniable, added to the fact that he knows the majority of the squad and the club's DNA, which will help him hit the ground running."
Wilder added: "Quite simply it was an opportunity which I just couldn't turn down. Just like in 2016, when this club comes calling, it is not something you pass up.
"This is Sheffield United, it is my team and I am thrilled to be back. We find ourselves in a difficult position, I understand that, but I think I can make a difference.
"When I received the call from Stephen (Bettis) asking if I would consider coming back to try and help, I didn't have to think about it. People know what this club means to me, and the task now is to try and provide a boost to improve our current situation.
"My relationship with Prince Abdullah and the board was repaired a long time ago. After some time passed following my initial departure, we spoke, met in person and there was an amicable ending. Now, coming back as manager, to know there is a united front again is crucial as we look to work together to improve the club's position in the Premier League."
Wilder has put pen to paper on a contract that will keep him at Bramall Lane until the summer of 2025, and he will oversee the first match of his second spell at home to title hopefuls Liverpool on Wednesday.