The hosts beat Bolton Wanderers away from home in the first round, while their visitors scraped past Leyton Orient in dramatic fashion at the beginning of November.
Barnsley began this season's FA Cup campaign with a tough trip to Bolton Wanderers in the first round earlier in November, and they went ahead early through a Ricardo Santos own goal, before Adam Phillips doubled their lead on the half-hour mark.
Jon Dadi Bodvarsson pulled one back for their hosts in the final 10 minutes, but Michael Duff's side stood strong to triumph on their travels and advance to the second round, before strengthening their promotion bid in League One with back-to-back three-point hauls in the following two encounters.
Michael Duff's side firstly triumphed away at Shrewsbury Town before hosting MK Dons last weekend and moving into the playoff spots with a 3-1 victory, as Phillips was again on the scoresheet between goals from Jordan Williams and Herbie Kane.
The Tykes now come into the weekend on the back of a cup defeat, though, as their EFL Trophy campaign ended with a 2-1 defeat away at Port Vale in the second round on Wednesday, with Tom Edwards's 73rd-minute goal not enough to spark a comeback.
Before they turn their focus back to their fight for an immediate promotion back to the Championship this season, Duff's men are tasked with seeing off fourth-tier opposition at Oakwell on Saturday in order to book their place in the third round of the FA Cup.
Their visitors, meanwhile, will make the trip hoping to cause a major upset, having already pulled off an impressive result to reach this stage, as they took on League Two leaders Leyton Orient in the first round.
That game at Gresty Road looked set to end goalless and go to a replay, but Bassala Sambou popped up with a 92nd-minute winner to ensure his side advanced and avoided a trip to East London for a return fixture.
They now face another unenviable tie against one of the strongest sides currently in the competition, but the Railwaymen will travel with extra confidence following their first-round win, having also put up back-to-back victories in League Two, firstly beating Colchester 1-0 before Dan Agyei hit the only goal away at Swindon Town last weekend.
Having now climbed to 15th spot after a difficult start to the campaign, Lee Bell's side will aim to keep building momentum with what would be an eye-catching triumph away at the League One promotion-chasers.
Barnsley FA Cup form:
Barnsley form (all competitions):
Crewe Alexandra FA Cup form:
Crewe Alexandra form (all competitions):
Barnsley heavily rotated their squad for the EFL Trophy contest away at Port Vale, but we should see the Tykes revert to their strongest starting XI on Saturday, with Mads Andersen and Tom Edwards set to rejoin Liam Kitching in a back three from the outset.
Further forward, Devante Cole will come back in to lead the line, while Slobodan Tedic remains doubtful due to an injury, meaning James Norwood could earn a first start following his return to fitness unless Jack Aitchison is preferred.
Luca Connell has been a key man in midfield since arriving from Celtic in the summer, and he should again play in the engine room alongside Herbie Kane and Adam Phillips after both got on the scoresheet in their recent league win over MK Dons.
Crewe Alexandra will likely remain without danger man Courtney Baker-Richardson, who has been out of action since the beginning of November after netting seven goals in his first 15 league appearances of the season.
In his absence, Dan Agyei will be relied on to lead the line, while Bassala Sambou should also feature in the attack after netting the winner in the first round.
Luke Offord has been a mainstay in the Railwaymen defence so far this season, and he should again partner Billy Sass-Davies in the middle of a back four.
Barnsley possible starting lineup:
Collins; Edwards, Andersen, Kitching; Williams, Kane, Connell, Phillips, Cadden; Cole, Norwood
Crewe Alexandra possible starting lineup:
Okonkwo; Mellor, Offord, Sass-Davies, Uwakwe; Brook, Thomas, King; Tabiner; Agyei, Sambou