Team Giant-Shimano rider Kittel, who is 22nd overall, did not seem to be well-placed for the final sprint but overhauled Ben Swift and Elia Viviani in the last few metres to win the stage in dramatic style on his 26th birthday.
"It was close. Actually I thought I lost the race already because I was really in a not good position," Kittel told reporters after crossing the line.
In the overall standings, Matthews, of Orica-GreenEdge, is eight seconds clear of Italian Alessandro Petacchi with Daniel Oss, another Italian, a further two seconds back in third.
The race returns to Italy with the fourth stage on Tuesday, a flat 112-km ride from Giovinazzo to Bari.
(Reporting By Brian Homewood; editing by Josh Reich)
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