The sides had finished goalless after 90 minutes, forcing the match into the drama of sudden death spot-kicks and it was Scotland who prevailed.
Earlier, City midfielder Weir had been at her incisive, inspirational best during a competitive first half at La Manga.
Her probing passes and vision and skill caused the Hungarians no end of headaches, but Scotland were unable to find a cutting edge in front of goal.
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With crucial domestic games on the horizon – not least Sunday’s FA Cup fifth round derby at Manchester United - Weir was one of four Scotland players substituted after a goalless opening half.
However, neither side was able to make a subsequent breakthrough forcing the tie to be settled by a penalty shoot-out.
And Pedro Martinez Losa’s Scots emerged the victors to end their Pinatar Cup campaign on a victorious note after having earlier beaten Slovenia but lost to Wales.
