The Donegal goalkeeper was called into action several times in the first half of a game where the kick-off was delayed due to thunderstorms.
In the 17th minute Dzsudzsak tried his luck from distance and Given did well to get down and take it first time.
Within a minute Given stops the same Hungarian striker with another smart save.
And it wasn’t third time lucky in the 24th minute as Dzsudzsak fired another shot on goal, but again the Lifford man made the save.
Kieron Westwood came on for the second half, but Ireland manager Giovanni Trapattoni was happy with Shay’s efforts.
Westwood also pulled off some fine saves in the first 15 minutes of the second half.
Shay looked relaxed in a tracksuit on the bench in the second half.
Ireland had a much better second half, creating several chances.
And they had the ball in the net after a combination between Walters and Keane, but the goal was wrongly ruled off-side.
A good workout for Ireland though.
“We were a little bit lucky, because in the first half we could have gone two nil down but Shay Given was terrific,” Trapattoni told a news conference.
“Our opponents deserved to go ahead, and at the end we could have lost three nil. Hungary are quite a strong team, with good youngsters, playing some nice football.”
Ireland team: Given, O’Shea, Dunne, St Ledger, Ward, Duff, Andrews, Whelan, McGeady, Keane, Doyle.
Subs: 16 Westwood, 12 Kelly, 14 Walters, 15 Gibson, 17 Hunt, 18 O’Dea, 19 Long.