The world number 11, one of the outright favourites to win the tournament, breezed through the first set with one dropped leg, before turning up the heat in the second set with a 100.2 average and 100 per cent record on the doubles.
Hayter would claim her second leg to kick off the third set with a decent hold of throw, but she was unable to capitalise on some wobbles in Rock's finishing, particularly struggling with the bullseye.
Still, a 32 checkout made things interesting at 2-1 in the set, followed up by five perfect darts on her way to a key break in 14 darts that kept her in the contest.
Hayter suddenly found herself back in the frame in a fast-paced fourth set with both players holding their throws to make it 2-2 in legs.
With darts in hand, Rock kept up the frantic speed of play and rounded off the match with a 14-dart finish via tops to book his place in round two.
Rock averaged 90.18 for the match, hitting three 180s. Both players hovered around finishing a third of their doubles.
'I let off the pedal'
"I was definitely nervous," Rock told Sky Sports after the win.
"I let off the pedal a wee bit, maybe underestimating her, that's not me being disrespectful, that's just the way I was thinking.
"I'm a numpty for thinking that way! I will give myself a kick up the backside because I can't do that again.
"At 2-0 up, I thought I was cruising, but that could have gone 2-2. A bit of my fault to let her back in.
"There's been a lot of underdog stories, especially yesterday, so in my head I was like 'just get over the line'."
Australia's Joe Comito awaits Josh Rock in the next round.
Gates dances into round two
Leonard Gates, a crowd favourite at Alexandra Palace, overcame a challenging match against Mickey Mansell to advance to the next round of the World Championship.
In a subdued match marked by frequent breaks of throw, Gates took the first set 1-0 before Mansell won three consecutive legs to level the score in the second set.
Gates regained momentum to win the third set, with both players averaging in the low 90s as they entered the fourth.
With a match low on maximums, Mansell needed a response but saw his doubles efficiency begin to evaporate, as both players saw their averages unravel in the fourth set.
Mansell eventually won the leg with a 33-dart break of throw, though both players' averages dropped to around 50 for the set.
A 12-dart hold offered some brief reprieve for Gates before the Northern Irishman took out 56 to send the match to a deciding set.
Despite the advantage of having the darts first, Mansell's game swiftly fell apart as he was twice broken by Gates, with the Texas-native storming the fifth set via three missed match darts to eventually take the match 3-2.
Gates will next face the winner of the match between Nathan Aspinall and Lourence Ilagan.
Doets sets up Munyua clash
In the session opener, Kevin Doets came through a hard-fought match against Matthew Dennant to set up a "dream" second-round clash with Kenya's David Munyua, who upset world number 18 Mike De Decker on Thursday.
Doets began with a 152 checkout, but Dennant, making his debut, claimed the first set by hitting all of his double attempts.
The Dutchman rallied, however, resisting constant pressure to clinch the following three sets en route to a 3-1 victory, averaging 92.11 for the match.
Elsewhere, Englishman Ryan Meikle dropped just a single leg in his 3-0 rout of Jesus Salate - the first Argentinian to play at the worlds - as the world number 62 reached the second round for a fourth year in a row.
Meikle will face New Zealand's Jonny Tata in the next round.
Friday's evening session rounds off the first-round action at this year's PDC Darts World Championship, with Nathan Aspinall and Beau Greaves both in action.
Friday afternoon session results:
Kevin Doets 3-1 Matthew Dennant
Mickey Mansell 2-3 Leonard Gates