The Blades picked up just their sixth victory of the season last time out, and they will aim to finish the season strongly to build momentum for their return to the Championship next season.
Newcastle suffered a narrow 4-3 defeat on Friday in an eye-catching encounter with new champions Manchester City at St James' Park.
The Magpies went ahead through Emil Krafth in the 25th minute, but goals from Joao Cancelo and Ferran Torres turned the game on its head late in the first half, before a Joelinton penalty in the sixth minute of added time saw the sides go into the break level.
Despite falling to an eventual defeat, the Tyneside outfit will feel positive about coming close to a result against the league's runaway team, while they have displayed strong form in the last six weeks to move themselves away from the threat of relegation.
Since the beginning of April, the Magpies have picked up a commendable tally of 11 points from seven Premier League games, including a 3-2 win over seventh-placed West Ham United and a recent 4-2 victory over third-placed Leicester City, as Willock and Paul Dummett got on the scoresheet alongside a Callum Wilson brace.
As a result of their upturn in form, Bruce's side recently managed to confirm their survival, having previously been in a battle with the likes of Fulham and Burnley to avoid the drop to the Championship.
They take on a side who have fallen well short in the battle to survive, as Sheffield United were officially relegated after a narrow defeat to Wolverhampton Wanderers in April.
The Blades were condemned to the drop having won just four of their 32 Premier League games at the time, picking up a poor tally of just 14 points.
While he did not manage to change their fortunes in time to form a serious survival bid, with five defeats from his opening five games, Sheffield United have arguably played with more freedom since the confirmation of relegation, having won two of the four matches since that 1-0 defeat to Wolves.
They started with a solid 1-0 victory over Brighton and Hove Albion at Bramall Lane, as David McGoldrick netted the only goal of the game, but a 4-0 defeat to Tottenham Hotspur and a 2-0 loss at home to Crystal Palace seemed to suggest that the Blades have taken another step back.
However, Heckingbottom's men bounced back with an impressive 1-0 away victory over eighth-placed Everton on Sunday, as 17-year-old Daniel Jebbison marked his first Premier League start with a goal in the seventh minute, while they went on to hold out for just their fourth league clean sheet of the campaign.
While they have had a particularly underwhelming campaign in the top flight, the Blades will hope to continue their improved form in the final two matches as they aim to build on their six Premier League wins for the season and gain more momentum going into the Championship.
Newcastle United will remain without key forward Callum Wilson for Wednesday's games, as he will miss the remainder of the season with a hamstring injury.
They did not overly struggle in front of goal in their talisman's absence against Manchester City though, as Arsenal loanee Joe Willock netted his fifth Premier League goal in his last five Premier League appearances from midfield.
Meanwhile, fellow centre-back Fabian Schar will also miss out as he serves the final match of his three-game suspension on Wednesday following a red card in their 2-0 defeat to Arsenal.
Bruce has struggled for defensive options in the absence of Lascelles and Schar, with Emil Krafth, Paul Dummett and Federico Fernandez lining up in a makeshift back three last time out.
That is not the end of Heckingbottom's issues, as Chelsea loanee Ethan Ampadu and forward Oliver Burke remain out while midfielder Sander Berge has suffered another setback in his return from injury and is likely to miss out on the trip.
Daniel Jebbison should start again after he impressed on his full debut with the winning goal, given the absence of McBurnie, Sharp and Burke alongside the poor form of record signing Rhian Brewster.
He will be joined by David McGoldrick, who has netted seven of the Blades' 19 Premier League goals this season.
Newcastle United possible starting lineup:
Dubravka; Krafth, Fernandez, Dumett; Murphy, Willock, Shelvey, Almiron, Ritchie; Joelinton, Saint-Maximin
Sheffield United possible starting lineup:
Ramsdale; Basham, Egan, Robinson; Baldock, Osborn, Norwood, Fleck, Stevens; Jebbison, McGoldrick
We say: Newcastle United 1-1 Sheffield United
Neither team come into this game with anything to play for with regard to the league table, but both will be hopeful of continuing fairly positive runs going into the final two matches of the season.
On this occasion, we cannot split the sides and back the Blades to be boosted by one of their best performances of the season last time out, inspiring them to pick up another result on Wednesday.
Watch the Sports Mole Football Shorts prediction for this game below: