2010 finalist Whitlock reached the second round for the first time in three years with a fabulous display of finishing against German qualifier Dragutin Horvat.
Horvat had earlier come from a set down to defeat Russia's Boris Koltsov 2-1 in their preliminary round tie, but had no answer to a fine performance from the number 17 seed.
The Australian, who has won two Players Championship events in 2016, ended the match with back-to-back checkouts of 170 and 158 as he set up a second round clash with Darren Webster, who defeated Whitlock at Ally Pally two years ago and at last month's Players Championship Finals.
"I've got revenge on my mind but I'll enjoy this win first," said Whitlock, who reached the semi-finals in 2014 when he last got past the first round stage.
"I'm really happy. I love a 170 as everyone knows, but I've been playing really well again recently and it feels like it's all coming good for me at the right time.
"I played well but I know I can play better and I will have to against Darren and if I go even further in the tournament."
Former World Grand Prix finalist Dolan averaged over 95 and took out a 102 finish in an assured display against Dutchman Kist, who reached a Players Championship final in 2016 but saw his campaign end in disappointment.
"I was happy with that - especially my finishing," said Dolan, who had a double success rate of 56 percent.
"I've struggled for 18 months but my form is coming back. I've got more determination, confidence and drive than ever before and I'm so pleased to get through.
"I've never really have had a good run here but on that World Championship stage, anything is possible."
Simon Whitlock (17) 3-0 Dragutin Horvat
Whitlock landed double 16 and double five to win the first two legs before Horvat fired in the match's first maximum and missed a dart at the bull for a 161 finish. Whitlock returned to peg double ten for the set after his opponent had missed two further attempts at double.
Whitlock took out 91 on the bull to break and then pinned double top. Horvat got a leg on tops but the Australian found the same target to move within a set of victory.
Whitlock hit a 180 and produced brilliant finishes of 92, 170 and 158 to seal a first round win for the first time in three years.