The Eagles memorably won 3-1 at Old Trafford earlier this season, but 17 points now separate the two sides in the table with Man United looking to further strengthen their Champions League hopes in midweek.
A controversially-rejected penalty claim against Callum Hudson-Odoi aside, there was little to shout about for either team during the stalemate - something which has been a feature of Man United's games against big-six opposition this season.
All five of those 0-0 draws this season have come against other members of the 'big six', and they have failed to find the back of the net in their last six such matches.
With 12 points now separating them from leaders Manchester City, it could be argued that Man United's record in those games is the biggest reason why their title challenge now appears to be all but over.
While Sunday's stalemate allowed Man City to move further clear, Man United escaped relatively unscathed in terms of those behind them, with Leicester City and West Ham United both losing in addition to Chelsea's dropped points.
Solskjaer's side remain second as a result, with a six-point cushion over fifth place, and they head into Wednesday's contest unbeaten in nine games across all competitions and with only one defeat in their last 20 Premier League outings.
Three of the last four of those have ended as draws, though, and the importance of returning to winning ways in midweek is only heightened by the looming Manchester derby awaiting them on Sunday.
Indeed, the Red Devils are heading into a potentially season-defining run, with their next five games after this seeing them take on Man City, AC Milan in both legs of their Europa League last 16, fellow top-four dwellers West Ham United in the Premier League and high-flying Leicester City in the FA Cup.
Man United will be favourites to go into that run off the back of a win as they travel to Selhurst Park unbeaten in their last seven visits to London and without defeat in their last 20 away league matches - a run which stretches back more than a year and one which has only been bettered four times in English top-flight history.
The 20-time champions have also never lost in 11 previous Premier League away games against Crystal Palace - the longest run of its kind ever seen in the competition - although Palace have won two of the last three league meetings home and away, which is as many wins as they had managed in their previous 27.
That includes their famous 3-1 triumph at Old Trafford in September, although their statistics from recent games suggest that they will struggle to repeat that three-goal haul on Wednesday.
Palace registered just 33 shots from five Premier League games in February - the lowest number by a team in a single Premier League month with at least five games since records began - including managing just six shots and facing 41 at the other end in their last two outings.
Nonetheless, Roy Hodgson's side have taken four points from those two games, somehow beating rivals Brighton & Hove Albion 2-1 while having just two touches in the opposition box, before holding out for a goalless draw with Fulham on Sunday.
Those results have lifted the Eagles 10 points clear of the relegation zone, and realistically two more wins would be enough to guarantee their safety for another season.
Palace may have to be patient for those wins considering nine of their final 12 games come against teams currently in the top half of the table, but Hodgson will be increasingly confident that the club's short-term future in the Premier League is secure despite his own future being far from it.
Crystal Palace Premier League form: WWLLWD
Manchester United Premier League form: DWDDWD
Manchester United form (all competitions): WDWWDD
Edinson Cavani was once again absent with a muscle problem, but the veteran striker has now returned to training and is expected to be in contention for this game.
However, Solskjaer is unlikely to take any risks over his fitness with the Manchester derby just around the corner, and if there is any doubt over a lingering injury then either Mason Greenwood or Anthony Martial will lead the line.
Eric Bailly, Alex Telles, Dean Henderson and Nemanja Matic are among the players knocking on the door, while Van de Beek, who scored his only Man United goal on his debut in the reverse fixture, will be hopeful of some game time too.
Hodgson voiced his frustration at having this match "thrust" upon his team at relatively short notice due to fixture rescheduling, particularly as it will likely prevent Wilfried Zaha from facing his former club.
The winger scored twice in the reverse fixture and has now returned to training, with Hodgson predicting that he will be back "very, very soon", although Wednesday's match may still come too early.
Zaha's probable absence is only the tip of the iceberg when it comes to Palace's injury troubles too, with the Eagles missing seven other first-team players for this match.
Crystal Palace possible starting lineup:
Guaita; Ward, Kouyate, Cahill, Van Aanholt; Milivojevic, Riedewald; Townsend, Eze, Ayew; Mateta
Manchester United possible starting lineup:
De Gea; Wan-Bissaka, Bailly, Maguire, Telles; Matic, Fred; James, Fernandes, Rashford; Cavani
We say: Crystal Palace 0-1 Manchester United
Manchester United's unbeaten record on the road is hugely impressive and we can see it extending here, although four of their last five away games have ended all square, while they have only scored three goals in that time.
We therefore do not expect to see a high-scoring Manchester United performance, but equally it is difficult to back a Palace side who have struggled to even get shots off lately, yet alone put the ball in the back of the net.
Watch the Sports Mole Football Shorts prediction for this game below: