The hosts continued their fine form with an excellent win at promotion-chasing Sheffield United on Friday, whilst the visitors were held to a draw during their best spell of the campaign.
Were it not for Derby County and Peterborough United also winning on Friday, Reading would have been all but safe ahead of the second game of the Easter weekend.
However, results elsewhere could not take the shine off an excellent defensive performance at a strong United side, who had not been beaten at home in their previous 12 games at Bramall Lane.
Lucas Joao netted his eighth league goal of the campaign in a first half that the Royals posed an almighty threat on the break, before Iliman Ndiaye's goal in the final minute of normal time looked to have broken their hearts despite defending so stubbornly in the second 45.
It is a result that kept Monday's hosts nine points clear of the relegation zone instead of six, so with only four games left to play, starting with Monday, Ince has led his side to the verge of survival during his successful temporary spell in charge.
The former Blackpool boss has now won four, drawn two and lost four of his 10 matches since being appointed on an interim basis, with three of those victories coming in their last five games.
Should Reading better Derby's and Peterborough's results on Monday, then they will move out of their reach, and should Barnsley suffer defeat and the Royals secure all three points, then the home side will mathematically confirm their stay in the second tier for next season.
Meanwhile, the visitors come into this game on the back of a strong run of form too, with Russell Martin's side putting together a six-game unbeaten streak.
After what has been a frustrating campaign of inconsistency during a transitional period under the former MK Dons boss, the Swans look to be finishing the season on a high ahead of a potential improvement next year.
The 1-1 draw with relegation-threatened Barnsley on Friday dented their slim chances of reaching the top six, with Monday's visitors occupying 14th place at the time of writing, and finding themselves seven points off the playoff places.
However, with a game in hand to come on many of the sides above them in the table, Swansea do retain a glimmer of hope of making a late charge for next month's playoffs, even if the possibility is not being discussed by Martin and his team.
Although, it is worth noting that the four games to follow their trip to Reading on Monday all come against promotion-chasing sides, but should the visitors record all three points at the Select Car Leasing Stadium and also triumph in their game in hand, then those slim hopes could certainly increase significantly.
Despite being forced off with a tight hamstring on Friday, Joao is expected to be available to lead the line once more for Reading here.
Fellow key starter John Swift remains unavailable with a calf injury though, and the midfielder could miss the rest of the season.
Yakou Meite is ahead of schedule in his recovery from an ankle injury, and so could feature from the bench to provide Ince with another option.
As for the visitors, with no fresh injury concerns to report from Friday's draw with Barnsley, Martin could well have a fully-fit squad to choose from.
Midfielder Flynn Downes was expected to return from a knock for just one of the two games over the Easter weekend, and after being left out of the squad on Friday, he should feature here.
Martin previously stated that he would rotate his side significantly between the two games, so a few changes are expected to his starting 11.
After making a game-changing impact off the bench last time out, Olivier Ntcham is expected to come in from the start.
Reading possible starting lineup:
Nyland; Holmes, Morrison, McIntyre; Yiadom, Laurent, Drinkwater, Rahman; Ince, Ejaria; Joao
Swansea City possible starting lineup:
Fisher; Cabango, Naughton, Manning; Christie, Downes, Grimes, Ogbeta; Smith, Ntcham; Piroe
We say: Reading 1-1 Swansea City
With both sides coming into this game on the back of some strong form, we can see them cancelling each other out in an even encounter on Monday.
Reading do not need to push for the win thanks to a healthy cushion above the relegation zone, so they are likely to settle for a point, whilst the visitors are expected to be rotated significantly, suggesting that they are not desperately pushing for the playoff places.
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