They will meet the winners of tomorrow’s tie between Fleetwood Town and Morecambe after captain Alfie Mawson’s successful spot-kick sent them through.
Barnsley were twice pegged back in normal time but former Tykes Craig Davies and David Perkins missed for the hosts in the shootout, when Conor Hourihane, Ivan Toney and Sam Winnall were also on target for the visitors.
Reds coach Lee Johnson said: “I thought we deserved to win. We worked really hard, hustled well and were a constant threat.
“It was just disappointing we had to go to penalties. Then it becomes a lottery and you’re looking to your players to dig in.”
League One survival is Johnson’s priority and he continued: “The two final legs are not until January, but, hopefully, we can get the town talking about that now. It’s back to the important league games and I’ll be seeking a similar performance to this at Colchester. We are bottom of the league, but we are much better than that as we’ve proved here. We are strong enough to go on a run to get us out of trouble.”
Barnsley had led at the interval after Adam Hammill struck from 20 yards in the 43rd minute.
Lewin Nyatanga bundled in an own-goal from a cross after the break but Newcastle loanee Ivan Toney headed home his first goal for the Reds in the 53rd minute.
Eight minutes from time, however, Will Grigg struck to take the tie straight to penalties.
Wigan Athletic: Jaaskelainen, Hendry, Barnett, Pearce, James (Wildschut 46); Perkins, Power, Jacobs (Flores 61), Kellett, Grigg; Revell (Davies 61). Unused substitutes: O’Donnell, Junior.
Barnsley: Davies, A White, Nyatanga, Mawson, Wabara, Hammill; Hourihane, Pearson (Bree 90), Watkins, Toney, Winnall. Unused substitutes: Ryan Williams, Jackson, Townsend, Isgrove.
Referee: K Hill (Hertfordshire).
Man of the match: Adam Hammill.