Li put her disappointing first round loss at the French Open behind her with a straight set win over Paula Kania in her opener at the All-England Club on Monday, and was looking to thwart the upset bid of Austrian No.1 Meusburger in their maiden clash on Wednesday.
Meusburger came into this encounter 0-9 against Top 10 opponents, with her lone Top 20 win coming over World No.15 Nathalie Dechy in a 2005 Fed Cup match.
The Turning Point
Li secured the match's first break to go up 3-2 in the first set and didn't surrender another game in the set. Li went up an early break in the second set before she was broken back, but from 2-2 she won the last four games of the match to complete her 6-2, 6-2 triumph.
By The Numbers
No category was Li more dominant in than winners, slamming 33 compared to four for Meusburger. She also broke serve six times, while only having her own serve broken twice. In fact, the Chinese won 61% of all of her receiving points, while Meusburger won 37%.
"I think the second round was better than the first because I already had a match under my belt," Li said. "Before my first round, I hadn't played in a month, so I was rusty. In the second match, I felt more comfortable about where the ball was going."
Li takes on Barbora Zahlavova Strycova, who pulled off a mild second round upset of Elena Vesnina. She is 2-0 against the Czech, with their previous two match-ups also occurring in Grand Slams.
"She is a smart player," Li said of Zahlavova Strycova. "She hits flat and plays well on grass. I just need to play my game, play more aggressive, come to the net as much as I can and follow the plan."