The No.1-seeded Wozniacki saved game points in three games - two in the first set, one in the second set - and ended up winning more than twice as many points as her shell-shocked opponent, 54 to 25.
She also blasted nine aces during the match, including three in one game at one point.
"I played well today and served very well," Wozniacki said after the match.
"I'm overall happy with my game, enjoying my time here and just looking forward to my next match."
"I played a good match today, but though the score looked easy, it was tough," Vinci said. "I had to stay focused the whole match, and I only arrived last night after a tough week on clay in Bucharest, so I only got to practice once on hardcourts before this match. But I like to stay aggressive, so it really suits my game here, and I'm confident I'll be able to achieve a good result here in Istanbul this week."
Vinci reached her first WTA final of the year last week in Bucharest, falling to the queen of the WTA Rising Stars, Simona Halep. Can Vinci, a former World No.11, keep her good form up this week?
"The draw is tough - there are some very good players here," she said. "I think I have a good chance to do well here because I'm the No.2 seed, but I'll just take it step by step and try to do my best."