ADO had won the first leg 5-1 but four second-half goals from Groningen on Sunday in a 5-1 win sent the match into extra time and penalties. On the 10th penalty, Groningen's Tim Matavz hit the bar.
Matavz had put Groningen ahead after 24 minutes by heading home a cross from Dusan Tadic. Before the break, Lex Immers equalised after Virgil van Dijk failed to clear the ball.
Groningen made an impressive start to the second half with Van Dijk scoring twice and Leandro Bacuna also on target to make it 4-1 within 15 minutes.
Matavz converted a penalty a minute before time to level the aggregate score to 6-6 after a handball from Mitchell Pique who was sent off.