Accrington defeated Crawley Town 4-1 to reach this stage, while non-league outfit Barnet overcame Chelmsford City after a replay.
Match preview
Given that they are competing in League One for the fifth successive season under manager John Coleman, Accrington will fully expect to beat Barnet at Crown Ground on Saturday.
Stanley have only twice made it beyond the second round of the FA Cup in Coleman's eight-year tenure, losing to Middlesbrough and Derby in the fourth round in the 2016-17 and 2018-19 seasons respectively.
While maintaining their place in the third tier will remain their priority this season - especially after a reasonably difficult start to the campaign sees them lying 19th in League One after 19 matches - Coleman will be keen to embark on another cup run, especially given the financial rewards progressing in this competition can bring to his club.
Having beaten potential relegation rivals Cambridge United 1-0 last weekend, they should head into Saturday's cup tie with plenty of confidence of putting their name in the hat for the third round, where plenty of Premier League glamour ties could await them.
However, Barnet should not be underestimated considering they will be making the trip to the North West off the back of four successive victories in all competitions.
Indeed, Dean Brennan's side have not conceded a goal in any of those wins, moving up to sixth in the National League table in the process as the Bees look to finish inside the play-off positions for the first time in three seasons.
Considering that Barnet have been fighting against relegation to the National League South in both of the past two campaigns, it has been quite the turnaround for the club in recent months.
They have pedigree in the FA Cup, too, having reached the fourth round of the FA Cup three times since the turn of the century, so Brennan will be hopeful of inflicting a sizable upset on Saturday.
Accrington Stanley FA Cup form:
W
Accrington Stanley form (all competitions):
L
D
W
L
W
W
Barnet FA Cup form:
D
W
Barnet form (all competitions):
L
D
W
W
W
W
Team News
Having beaten Grimsby Town in the Football League Trophy in midweek, Coleman will be keen to ensure his squad do not succumb to fatigue during a busy fixture period.
Captain Seamus Conneely should earn a recall to the starting XI having been rested on Tuesday.
Barnet, on the other hand, have had a full week between fixtures, so it would be a surprise if Brennan made any changes to the side which dispatched Torquay United last weekend.
Marvin Armstrong will be hoping to get himself on the scoresheet once again after proving to be the match winner in the 1-0 victory.
Accrington Stanley possible starting lineup:
Savin; Fernandes, Tharme, Rodgers; Clark, Conneely, Coyle, Longelo; Hamilton; Whalley, Leigh
Barnet possible starting lineup:
Walker; Wynter, Okimo, Collinge, Beard; Armstrong, Gorman, De Havilland; Kanu, Kabamba, Pritchard
We say: Accrington Stanley 2-1 Barnet
We expect Barnet to give Accrington a good fight on Saturday, but the League One side should have too much quality for their non-league opponents in the end.