In the 20th minute, Martin Devaney's cross was headed by Kevin Austin and Paul Reid volleyed the ball past Swansea goalkeeper Willy Guéret to make it 1–0.
Andy Robinson then scored in the 41st minute after Barnsley goalkeeper Nick Colgan failed to hold his weak strike.
No goals were scored in extra time, although both Lee Trundle and Adebayo Akinfenwa had chances for Swansea, and the game went to a penalty shootout.
The next three penalties were scored before Colgan saved from Alan Tate, ensuring a 4–3 victory for Barnsley and promotion to the Championship.
Barnsley's next season, during which their manager Andy Ritchie was sacked, saw them finish in 20th position in the Championship, two places and eight points above the relegation zone.
On 15 minutes, Knight doubled his tally and Swansea's lead, shooting past Nelson after receiving a through-ball from Leon Britton.
The Swansea goalkeeper Willy Guéret made a number of saves in the second half and the match ended 2–0, with his side progressing to the final with a 3–1 aggregate victory.
Martin Devaney's shot skimmed the Barnsley crossbar and Danny Schofield hit the post for Huddersfield.
After a goalless first half, Huddersfield's Gary Taylor-Fletcher scored from close range in the 85th minute, and the game ended 1–0 to the visitors.
Jon Worthington equalised seven minutes later when the ball crossed the Barnsley goal-line after he charged down a Nick Colgan clearance.
In the 78th minute, the Huddersfield goalkeeper Paul Rachubka failed to gather Brian Howard's shot and Daniel Nardiello scored, to send Barnsley to the final with a 3–2 aggregate victory.
[6] They had also played at the Millennium Stadium earlier in the year where they defeated Carlisle United 2–1 in the Football League Trophy final.
[15] Both teams adopted a 4–4–2 formation,[16] with both starting elevens remaining unchanged from their respective semi-final second-leg matches.
Devaney's cross was headed by Kevin Austin and Reid volleyed the ball past Guéret to make it 1–0.
Nardiello struck the set piece low, past a motionless Guéret, and into the Swansea goal to level the match at 2–2.
[15][17] Andy Ritchie, the winning manager, said "The players were absolutely magnificent and they deserve a great deal of credit ... We always felt that we could get a goal back when we were 2–1 down and at half-time we got them to focus.