The 29-year-old top seed, down at 10th in the ATP rankings after a disappointing year, will have been pleased at how he responded in the deciding set having been pegged back by Baghdatis and the two hours 40 minutes he spent honing his grasscourt game will serve him well.
Nadal began in rusty fashion, dropping serve early on and Baghdatis had chances to lead 5-2 with a double break but allowed the world number 10 off the hook.
A dreadful service game from Baghdatis allowed Nadal back into the first set and Nadal gradually began to find his range, taking the opener on the tiebreak.
Nadal saved two set points at 4-5 in the second set, the second with a deft drop volley, but could not fend off Baghdatis in the tiebreak as the match went the distance.
He took command in the decider though and moved through to the quarter-finals where he will face Australian Bernard Tomic.
(Reporting by Martyn Herman in London, editing by Pritha Sarkar)
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