The Kiwi broke serve in the 5th game and led 4-2 with Kvitova down a break point at 30-40, but she couldn't capitalise as the Czech held and won the next three games to take the opening et 6-4.
Kvitova had won their four previous matches, including a 6-4, 6-4 win in the second round at Roland Garros last year.
But Erakovic had reason to be confident going in, having had chances in that match a year ago, and having pushed Kvitova in a tight three sets defeat in Cincinnati a year earlier.
Unlike that match last year Erakovic quickly put behind her the disappointment of losing the first set by breaking serve in the first game of the second set and holding her next two service games to love.
A second break followed for a 5-2 lead and while the Kiwi was broken for 5-3, she continued to attack and broke to take the second set 6-3.
Erakovic held serve at the start of the decider but was broken with a sizzling Kvitova forehand winner in her next service game.
But down 2-1 Erakovic broke back immediately and the pair traded breaks until 4-4 in the final set.
With the tension rising both players stepped up with some scintillating shot making. But it was a Czech who struck the telling blow in the 9th game to break Erakovic's resistance.
Kvitova held to love to clinch her place in the second round.
The Czech committed 47 unforced efforts to Erakovic's 33. Both players had 15 break point chances converting six each.
Ultimately tennis is about results and Erakovic is left to contemplate another early exit this year. Apart from a semi-final appearance at the Pattaya Open in February, the Kiwi has made the second round twice and lost first round in six tournaments including the Australian Open and French Open.
But her level was better than we've seen in a long time and she returns to the grass courts of England soon, believing that on her favoured surface she can rejuvenate a career that has been stagnating.
Erakovic still has the doubles to contemplate playing with Britain's Heather Watson.
The pair open their campaign against third seeds Timea Babos of Hungary and Frenchwoman Kristina Mladenovic tomorrow.
Matt Brown travelled to Paris with Emirates Airline.