The League of Wales side took the salute from a capacity 2,500 crowd at Jenner Park on a lap of honour to cap another famous night in Europe to go with their victory over Latvia's Dynaburg in the preliminary round.
A team of former Football League players and youngsters, Barry were inspired by their player-coach, Garry Barnett, the 33-year-old former Oxford United, Fulham, Charlton and Huddersfield player who only took over at the club eight weeks ago.
Barry's general manager, Chris Aust, said: "If we drew Newcastle, they would bring 26,000 fans and we could hire Cardiff Arms Park for the home game. That would be my ideal scenario. We have already made enough money to keep me smiling over the next 11 months, but that would be icing on the cake."
Barry finally broke the deadlock on the night when the former Cardiff City striker Chris Pike converted a penalty after striker Tony Bird was held back by full-back Zoltan Molner. A minute after the break, they squared the aggregate score when Pike darted down the right and crossed for Dave O'Gorman to shoot home at the far post.
The Hungarians threw on all three substitutes and it paid off when Gabor Egressy found himself unmarked at the far post to score from the simplest of chances in the 63rd minute.
That put Barry 4-3 down overall, but in the 78th minute, a long clearance by their inexperienced goalkeeper Pat Mountain, in for the suspended Mark Ovendale, was flicked on by Pike. Craig Evans, a substitute, raced through to send the tie into extra time. When the penalties came Pike, Bird, Gary Lloyd and Evans kept their heads to seal victory.
Barry Town: Mountain; Johnson, Lloyd, French, York, O'Gorman, Barnett, Huggins, Ryan, Pike, Bird. Substitutes: Norman, Evans, Misbah, Griffith.
Vasas Budapest: Vegh; Komlisi, Molnar, Eros, Bukszegi, Stanici, Egressy, Zovath, Puzi, Pomper, Feher. Substitutes: Koszta, Bognar, Farkas, Csordas, Kaszas.
Referee: A Georgiou (Cyprus).Reuse content