The three-time champion Price needed to beat 2014 winner Chisnall in his final Group A match to advance and triumphed 5-4, throwing a 103 average.
Price had lost to Raymond van Barneveld 5-4 in Wolverhampton on Sunday to put his progress in doubt.
Van Barneveld thrashed Ted Evetts 5-0 on Monday to wrap up his group stage, while in Group B Simon Whitlock beat Christian Perez 5-3.
Also in Group B Mensur Suljovic lost 5-4 to Danny Noppert, while Joe Cullen beat Lisa Ashton 5-3, with Michael Smith a 5-1 winner over Ritchie Edhouse in Group C to reach the last 16.
Dirk van Duijvenbode beat Adam Gawlas 5-3 in Group D, while Rob Cross survived a scare to book his place in the knockout stage as he came from 3-0 and 4-2 down to beat Martin Schindler.