Australian Open champion Li arrived at the All England Clubon the back of a dismal clay court season, concluding with a first-round exit at last month's French Open, her worst display at a grand slam for three years.
The Chinese world No.2 struggled in her first match against qualifier Paula Kania, but showed signs of a return to form against Meusburger, dictating play from the baseline with a range of powerful groundstrokes that have become her trademark.
Li broke the current world No.38 in the fifth game and went on to win the next four to take the first set and break again early in the second.
Meusburger battled back with a break of her own to level the set, only for two-time grand slam champion Li to reel off the last four games to secure her place in the third round.
The three-time Wimbledon quarter-finalist will next play either Czech Babora Zahlavova Strycova or 32nd seed Elena Vesnina.
(Editing by David Goodman)
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