The home side disposed of Arsenal Under-21s to reach this stage, while the visitors also posted a notable win in seeing off Bristol Rovers.
Match preview
Having put together a nine-match unbeaten run in all competitions, Peterborough would have been confident of causing a surprise against Leeds United in the FA Cup.
Instead, Darren Ferguson's side succumbed to a 3-0 defeat at home to the Yorkshire giants, powerless to prevent a piece of genius from Patrick Bamford along the way.
All things considered, it was a tame ending to Peterborough's FA Cup campaign, yet Ferguson will be largely content to focus on other priorities during the second half of the season.
Sitting four points adrift of League One leaders Portsmouth with a game in hand, Posh are well placed for promotion, but Ferguson will also want to reach Wembley through this competition.
Victories over Tottenham Hotspur Under-21s and Arsenal Under-21s have been recorded along the way to the last 16, and expectation is growing after seemingly being provided with a favourable draw.
Crawley will have something to say about that having already defeated League One opposition on two occasions in this season's competition, as well as Aston Villa Under-21s.
Scott Lindsey is approaching a year in charge and the consensus is that Crawley are performing as well as they have done for some time, winning eight of their last 13 games in all competitions.
An early FA Cup exit meant that they were in league action at the weekend, recording an impressive 4-2 victory away at Bradford City.
After prevailing in three of their last four league fixtures, Crawley sit in ninth position, only outside of the playoff places on goal difference.
Peterborough United EFL Trophy form:
W
W
L
W
Peterborough United form (all competitions):
W
W
D
D
W
L
Crawley Town EFL Trophy form:
W
L
W
W
Crawley Town form (all competitions):
L
L
W
L
W
W
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Team News
While Ferguson is expected to make some alterations on Wednesday, they may not be as wholesale as some may anticipate.
Romoney Crichlow, Ryan De Havilland and Malik Mothersille will all feel in line to be handed an opportunity from the start.
Meanwhile, Lindsay could opt to hand an outing to Klaidi Lolos after he made an impact as a substitute in the win over Bradford.
Goalkeeper Luca Ashby-Hammond, who has made nine appearances this campaign, may also be brought back into the side, and Kellan Gordon is an option at right wing-back.
Peterborough United possible starting lineup:
Talley; Katongo, Knight, Crichlow, Burrows; De Havilland, Collins; Poku, Randall, Mason-Clark; Mothersille
Crawley Town possible starting lineup:
Ashby-Hammond; Williams, Conroy, Maguire; Gordon, Kelly, Campbell, Tsaroulla; Darcy, Orsi, Lolos
We say: Peterborough United 3-1 Crawley Town
With both teams likely showing ambition to reach Wembley now that they have reached this stage, we expect full-strength sides to be named. However, that will only benefit Peterborough, who we think will record a relatively comfortable win on home territory.