The visitors, meanwhile, only have a one-point cushion inside the play-off spots after suffering defeat to their local rivals Cambridge United at the weekend.
Match preview
Having punched considerably above their weight to become a stable mid-table side in League One across recent seasons, Accrington's five-year stay in England's third tier is at serious risk of coming to an end.
Seven defeats in their last nine league matches - with only one win against Port Vale to show for themselves during that run - has seen John Coleman's side fall to second-bottom in the table after being thrashed 5-2 by Fleetwood Town on Saturday.
Trailing 2-0 at half-time and at a man's disadvantage following Liam Coyle's dismissal four minutes into first half injury-time, Coleman would have taken a small amount of satisfaction from his players' spirit to score two goals after the break, with two injury-time efforts from the visitors compounding Accrington's inferior goal difference compared to their rivals.
Indeed, with Oxford United and Cambridge both two points ahead of Stanley either side of the dreaded dotted lines, Accrington require a favour from Portsmouth and Wycombe Wanderers respectively on Tuesday if they are to have a chance of moving outside of the bottom four positions in midweek.
On current form, though, it is going to require a monumental effort from everyone on and off the pitch at Crown Ground in order for them to collect the three points which they so desperately require against Peterborough.
Having won six of their previous eight away trips in League One prior to visiting Abbey Stadium for Saturday's lunch-time kick-off, Peterborough would have been confident of dispatching one of their fiercest rivals.
However, goals either side of half-time from Harrison Dunk and Sam Smith gave the hosts a priceless victory, which moved them level on points with 20th-placed Oxford, while reducing Posh's chances of finishing inside the play-off positions in the process.
Darren Ferguson's side's excellent form of late has still provided themselves with an excellent chance of snatching a play-off spot, though, with Bolton Wanderers and Derby County a point either side of them in fifth and seventh positions respectively.
With tough fixtures against automatic promotion contenders Ipswich Town and Barnsley still to come for Peterborough, claiming all three points away to Accrington on Tuesday feels like a necessity if they are to achieve their primary aim for the campaign and remain in the hunt for an instant return to the Championship.
Accrington Stanley League One form:
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Peterborough United League One form:
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Team News
Accrington will be without Coyle due to suspension after his red card against Fleetwood at the weekend, with Mo Sangare set to replace him in the hosts' engine room.
Joe Williams and club captain Seamus Conneely are unlikely to be involved due to injury, but Tommy Leigh and Ethan Hamilton returned to start against Scott Brown's side in a massive boost for Coleman as he attempts to keep the club up.
Ferguson, meanwhile, may be tempted to make a few changes after his side's dismal performance in the defeat to Cambridge only three days prior to making the trip to the North West.
Dan Butler and Josh Knight could be called upon in an attempt to tighten the visitors' defence following some soft defending against their rivals, but Peterborough's offensive unit is unlikely to be tampered with given the amount of goals they have been scoring across previous games.
Accrington Stanley possible starting lineup:
Jensen; Clark, Nottingham, Tharme, Rodgers; Hamilton, Sangare; McConville, Whalley, Leigh; Pressley
Peterborough United possible starting lineup:
Norris; Thompson, Knight, Edwards, Butler; Ward, Norburn, Taylor, Mason-Clark; Clarke-Harris, Poku
We say: Accrington Stanley 0-2 Peterborough United
With two of Peterborough's final three fixtures coming against impressive sides above them in the table, Ferguson and his players will be more than aware of the importance of claiming all three points against Accrington on Tuesday.
Likewise, time is running out for Coleman's side to save themselves from relegation, but they are likely to be outclassed in their next match and fall to an eighth defeat in 10 matches.