Played in warm conditions with a breeze, both players held serve in the opening games of the final set before Erakovic was broken and then Vesnina, ranked at 56 in the world, compared to Erakovic's 82, traded service holds until 4-2 to the Russian.
Erakovic then served a double fault to give Vesnina a 5-2 lead before breaking her opponent's serve to love, which was perhaps an indication of the match, one moment a high and the next a low.
Erakovic was able to add one more game to her tally before Vesnina wrapped up the contest 6-4. Erakovic had been hoping to continue her run at the tournament where she beat former champ Svetlana Kuznetsova in the first round, her first singles victory at the US Open.
"I had my chances but also gave myself a chance. It's a learning curve. In the last three or four years I don't think I've been as well in the mental game."
Erakovic and Spanish partner Arantxa Parra Santonja take on Spaniards Garbine Muguruza and Carla Suarez Navarro in the doubles second round.
"It's lots of fun to play with Arantxa. So hopefully we can play some good tennis in our next match."
In the doubles there was better news as Mike Venus secured a win with his partner Mikhail Kukushkin of Kazakhstan 6-2 3-0 retired over Spain's Feliciano Lopez and Juan Monaco, the latter retiring with a wrist injury.
"It would have been great to finish the game, but it was just good to win. We started out tentative but played better the more we were out there," said Venus, who has competed in all four Grand Slams in doubles this year.
They now play the Italian pair of Daniele Bracciali and Andreas Seppi.