Watson won 6-2 6-4 to set up a meeting with German 25th seed
The 20-year old Briton started strongly on serve and made the first breakthrough on the Russian’s serve in game four, getting excellent power into her returns from a crouched position.
She maintained her dominant serve – she sent down five aces in the match compared with the slower Vesnina’s none, while not committing a double fault against the Russian’s three – to win the set and started strongly in the second.
However she was unable to convert a break point in the second game then found herself break down in the next, saving one break point but hitting the next too long to hand her opponent the advantage in the set.
The British number three responded magnificently, breaking straight back with a backhand winner flicked across the court following a Vesnina drop-shot.
She then held and broke again, seeming on course for the victory at 4-2 up, only to immediately hand Vesnina a straightforward break back.
Qualifier Watson is made of stern stuff – she reached the second round here in 2011, becoming the first British woman to do so since 1994 – and she attacked the Vesnina serve to give herself the chance to serve for the set.
And she held her nerve to do so, Vesnina striking into the net to see her record at Roland Garros slip to one win and six defeats.
That poor record should not take away from Watson, whose performance on Court 6 is an encouraging sign that her career is progressing.
The British number two, who like fellow first-round loser Elena Baltacha was put straight into the main draw, suffered an atrocious start. She only held when 5-0 down.
In the second set she was broken for 2-1 before establishing her serve at a more competitive level; however by then it was too late and she was eventually broken again for 5-2.
She forced only one break point in the match. Czink, ranked 16th in the world to the Briton’s 81, will next play