The 24-year-old struck in the in the 63rd and 67th minutes to lift his side to 65 points and an unassailable 10-point lead in the standings with three games left to play.
With closest rivals Soenderjyske suffering a 3-2 loss to third-placed Midtjylland on Saturday, FC Copenhagen knew that a home win would be enough to become champions for the first time since 2013.
But they failed to break the deadlock in the first half despite a number of decent chances.
Santander changed all that when he turned and fired home to give his side the lead. He had just enough time to be booked for removing his shirt in celebration before adding a second.
The Paraguayan's goals sparked a beer-drenched celebration at the final whistle as Copenhagen's Norwegian coach Stale Solbacken won his sixth Danish title and his first since returning to the club for a second spell in 2013.
(Reporting by Phillip O'Connor, editing by Ed Osmond)
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