Aspinall was appearing in only his second European Tour final after being beaten by Michael Smith in the 2023 German Darts Grand Prix.
He earlier hit a stunning 170 checkout in the semi-finals against Gary Anderson to force a deciding leg.
That followed a 6-1 thrashing of world number one Luke Humphries in the quarter-finals and a 6-5 win over Jermaine Wattimena in the third round on Sunday.
Joyce, 39, beat former world champion Rob Cross 6-4 in the third round before a 6-3 win over Scotland’s Cameron Menzies.
He then stunned Van Gerwen 7-5 after the three-time world champion had beaten Gerwyn Price 6-4 in the quarter-finals, despite the Welshman averaging 107.4.
World champion Luke Littler did not enter the event in Gottingen.
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