Whitlock whitewashed Colin Osborne, hitting a stunning 164 finish and averaging over 95 in the process, while van Barneveld defeated Brendan Dolan 4-1.
The pair could meet in the quarter-finals of the £1 million pound tournament should they both win their third round games.
Whitlock faces Dave Chisnall on Thursday 27 December, when ‘Barney’ will take on Gary Anderson.
Mark Webster was denied a place in the third round by Colin Lloyd.
Sunday sees the completion of round two with James Wade facing Steve Beaton in the afternoon session and Vincent van der Voort up against Dean Winstanley, before Michael van Gerwen takes on Peter Wright in the evening.
The third round also kicks off as Robert Thornton takes on Phil Taylor in the final match before the Christmas break.
By Chris Murphy
Images courtesy of Lawrence Lustig/PDC