The French sixth seed got off to a shaky start but backed by the Philippe Chatrier Court's partisan crowd, played more aggressively to unsettle his Cypriot opponent.
Baghdatis, like Tsonga a former Australian Open runner-up, lost his composure as he failed to cope with the noisy crowd and gradually slipped out of contention.
Tsonga, looking to become the first French man to win Roland Garros since Yannick Noah in 1983, next faces Latvia's Ernests Gulbis.
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(Reporting by Julien Pretot; Editing by Ed Osmond)
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