The two sides went into tonight's second leg locked at 1-1, and they played out the same scoreline on the night to force penalties, which Barnsley won 4-2 to set up a Wembley showdown with Oxford United in April.
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Maxwell continued to be the busier of the two goalkeepers, being forced into further saves to deny Josh Brownhill and Conor Hourihane, while also watching a Winnall header drop narrowly wide of the target.
Barnsley were the more dominant side in the second half too, though, and twice came close through Adam Hammill before the hour mark, first seeing his curling effort saved by Maxwell before blazing one over the top from 20 yards.
The opening goal on the night finally arrived with just over 20 minutes remaining as Barnsley won the ball back before Winnall found Hourihane, who tucked his finish past the keeper to send his side on course for Wembley.
Fleetwood would have something to say about that, however, and the hosts levelled things up again both on the night and on aggregate in the 81st minute when substitute Adam Hunter showed good feet inside the box before firing past Davies.
There were chances for both sides to win it late on, with Ashley Fletcher playing one ball right across the six-yard box with no takers, before nodding wide with the goal gaping in the very last seconds of the match. Sandwiched between those openings was a free header for Nathan Pond that was blocked on the line.
Neither side could find a winner, however, as the match went straight to penalties, where Hammill scored the decisive spot kick to book Barnsley's place in the final.body check tags ::