Fleetwood Town 1 Barnsley 1 (Agg 2-2 - Tykes win 4-2 on penalties) Wembley awaits Tykes after dramatic win on penalties
The teams had gone into the second leg after drawing their first meeting at Oakwell 1-1 last week.
And it ended all-square again at the end of normal time at Highbury.
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Hide AdConor Hourihane had put the Tykes ahead in the 67th minute to make it 2-1 on aggregate but, 10 minutes from time, the hosts levelled through substitute Ashley Hunter.
With no extra-time in the competition, it went straight to penalties, with Barnsley goalkeeper Adam Davies saving two spot-kicks from Fleetwood’s Conor McLaughlin and Amari Bell.
That enabled Hammill to fire in his effort off the underside of the bar to make it 4-2 and send the travelling fans from South Yorkshire into raptures.
Barnsley will now face Oxford United in the final on April 3.