Chris Dobey was another second-round casualty, as the eighth seed was beaten 3-1 by Andrew Gilding.
Despite dropping the first set, Gilding landed a 10-darter to clinch a crucial third before defying a 167 checkout by Dobey in the fourth to celebrate an eye-catching win.
"I feel amazing," Gilding told Sky Sports. "I felt really bad in practice, that's usually a good sign, you can only get better from there.
"The first thing I wanted was a nine-darter and the second was a win, so I got the second one."
Bunting recorded a straight-sets victory over India's Nitan Kumar, landing three ton-plus checkouts and conceding just two legs.
Kumar was unable to emulate the performance that saw him stun Richard Veenstra, as Bunting capped off a professional display with a 53% success rate on the doubles.
“I felt really comfortable tonight,” said Bunting. “I know how well Nitin can play. I’ve played him a few times before, and what a fantastic ambassador he is for our sport.
“He’s only going to go from strength to strength, but I’m so happy with the win."
Meanwhile, 2023 world champion Smith was defeated 3-1 by the Netherlands' Niels Zonneveld, who will now take on Jonny Clayton for a place in the last 16.
Smith was made to pay for a missed set dart in the third as Zonneveld held his nerve with a series of sharp finishes to seal a landmark triumph.
Pietreczko fights back as Sakai exits
Ricardo Pietreczko staged a stirring fight-back to beat David Chisnall 3-2 earlier in the day, as the 31-year-old German held his nerve in a dramatic tie-break after Chisnall missed a match dart.
Ryan Searle was far more clinical, as the 20th seed swept aside Brendan Dolan 3-0 with a ruthless barrage of heavy scoring.
There was no fairytale for Japanese crowd favourite Motomu Sakai, though, as he was outclassed 3-0 by composed Swede Andreas Harrysson.
Elsewhere, Dirk van Duijvenbode also exited after James Hurrell produced a superb display to claim a pulsating 3-2 win over the Dutchman.
Read our full report on Saturday's afternoon session
Results
Afternoon session
Ryan Searle 3-0 Brendan Dolan
Andreas Harrysson 3-0 Motomu Sakai
James Hurrell 3-2 Dirk van Duijvenbode
Ricardo Pietreczko 3-2 Dave Chisnall
Evening session
Niels Zonneveld 3-1 Michael Smith
Andrew Gilding 3-1 Chris Dobey
Stephen Bunting 3-0 Nitin Kumar
(Jonny Clayton advanced by walkover after Dom Taylor was disqualified.)