Colombian Nairo Quintana (Movistar) finished second overall, 31 seconds behind, and Italian Vincenzo Nibali (Bahrain-Merida) took third place, 40 seconds off the pace, according to provisional results.
"It's really crazy, I cannot describe it with words. It was such a nerve-racking day but I did it, I had good legs," said Dumoulin.
The 26-year-old time-trial specialist turned grand tour rider had flagged himself up in 2015 when he took sixth place overall in the Tour of Spain.
He lost the Giro overall leader's pink jersey on the 19th stage as he struggled in the final mountain stages but limited his losses to be in a good position for Sunday's 29.3-km solo effort between Monza and Milan.
Dumoulin finished second behind compatriot Jos van Emden (LottoNL-Jumbo) in the stage but his rivals for the overall win ended up far behind.
Frenchman Thibaut Pinot (FDJ) took fourth place overall ahead of Russian Ilnur Zakarin (Katusha).
(Writing by Julien Pretot; Editing by Clare Fallon)
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