The hosts beat Fleetwood Town 3-2 in the first round, while Crewe got the better of Sunderland in a penalty shootout.
Match preview
Since beginning the campaign with a demoralising 7-0 defeat to Barnsley, Port Vale have shown immense character to embark on a five-game unbeaten run.
That impressive run of results began with a win over Fleetwood Town in the EFL Cup, giving them the confidence to go on and claim 10 points from their next four league matches.
In their most recent encounter, a 50th-minute strike from James Wilson guided Port Vale to a narrow 1-0 win over Carlisle United, ensuring the Valiants finished the weekend in sixth position.
Having won all three of their competitive games at Vale Park this season, Andy Crosby's side will be aiming to make full use of home advantage once again on Tuesday.
The Valiants have the opportunity to reach the third round of the EFL Cup for the first time since the 2009-10 season.
Meanwhile, Crewe Alexandra will be looking for a response after they suffered their first defeat of the season at the weekend.
Crewe picked up six points from their opening four league games, before they made the trip to Valley Parade for Saturday's meeting with Bradford City.
The Railwaymen trailed at the break following Jamie Walker's 43rd-minute opener, and they were unable to find a way back into the contest in the second half, representing the first time they have failed to score this season.
While Crewe were unable to trouble the scorers on Saturday, they will still be confident of finding the net on Tuesday after racking up 10 goals in their opening four league matches.
Like their hosts, Crewe are hoping to end their long wait for a third-round appearance, as they look to progress from the second round for the first time since the 2009-10 campaign.
Port Vale EFL Cup form:
W
Port Vale form (all competitions):
L
W
W
D
W
W
Crewe Alexandra EFL Cup form:
W
Crewe Alexandra form (all competitions):
D
W
D
W
D
L
Advert - content below:
Team News
Midfielder Tom Conlon is a long-term absentee for the hosts, while there are doubts over the availability of Ellis Harrison and Kofi Balmer.
After arriving on loan from Tottenham Hotspur, Alfie Devine made his Port Vale debut as a substitute against Carlisle, and he could be presented with his first start for the club on Tuesday.
Ben Garrity dropped down to the bench for Saturday's victory, but he is expected to return to the side for the midweek cup tie.
As for the visitors, Courtney Baker-Richardson could be included in the matchday squad, having returned to training following an injury issue.
Defender Zac Williams could be recalled to the starting lineup after dropping out of the side for Saturday's defeat to Bradford.
Elliot Nevitt, who has scored twice in Crewe's last three games, will continue to lead the line for Lee Bell's side.
Port Vale possible starting lineup:
Ripley; Cass, Smith, Iacovitti; Clark, Arblaster, Ojo, Plant; Devine, Garrity; Wilson
Crewe Alexandra possible starting lineup:
Davies; Offord, Demetriou, Williams; Cooney, Powell, Tabiner, Demetriou, Adebisi; Tracey, Long; Nevitt
We say: Port Vale 2-0 Crewe Alexandra
Port Vale are currently enjoying an impressive run of form, having won four and drawn one of their last five competitive matches.