Unseeded Begu, 22, broke her 16-year-old opponent once in the opening set and twice to one in the second before serving out the match.
World number 87 Begu said her ability to maintain a strong first serve earned her the title, having won 74 per cent of those points.
''My service was what got me through,'' she said ''I was a little worried when Donna came back from 2-4 to level the scores at 4-4 in the second set, but I managed to break her immediately.''
''It feels great to win a title. I'll take back sweet memories from Tashkent.
"I'm glad I made a decision to play the event at the last moment, and will surely come back to defend my title.''