Begu stamped her authority on the final when she reeled off eight games in a row to clinch the first set and lead 5-0 in the second before sealing a 6-3 6-1 victory.
"I think the key today was to stay calm and make my opponent run more, and I think I was successful in those. I was also hitting the balls deep and close to the lines," Begu said.
"I also think I was better on the important points -- I wasn't dominating every game, but I did better on the big points."
The win gave the 25-year-old her second WTA career title after she won the Tashkent Open in 2012 and will see her ranking climb to a career-best 26th.
"I'm so happy to win my first WTA title in three years -- it's been a long time, and I've improved a lot, I think," she said.
"I've learned a lot from many matches and many experiences, and most of all I think I've become much more consistent when I'm playing. I feel totally different from three years ago."
Sasnovich had to console herself by making her first WTA final. The Belarusian had to come through the qualifiers to get into the main draw, and had never made it to a quarter-finals of a WTA event before this week.
(Reporting by Julian Linden in Singapore; editing by Sudipto Ganguly)
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