Humphries - the world champion in 2024 - is seeking to regain the title after losing last year's final to fledgling rival Luke Littler and laid down his marker at Alexandra Palace on Saturday.
'Cool Hand' started brightly and despite facing a brief wobble in the third set, he closed out the match and recorded a 98.58 average and eight 180s.
"I was good at the start, I felt really good, but then in that third set I fell asleep, to be honest - I maybe relaxed too much," Humphries told Sky Sports afterwards.
"Credit to Ted, he got on me when I wasn't at my best, but I managed to find that special stuff in the end. I'm really pleased with the way I managed to come back."
Humphries made an ominous start, sweeping through the first set without a hitch and did not allow English compatriot Evetts a sight at double.
His dominance continued, with a monster 138 checkout highlighting a second stanza where he averaged an impressive 107.13.
Evetts, though, raised his level in the third with a tops finish to break the Humphries throw, before nailing it again at the fifth attempt to reduce the set deficit to 2-1.
The pair exchanged breaks in set four until Humphries turned the screw again, taking out scores of 41 and 23 on double 16 to seal his progression.
Lim makes history
Awaiting Humphries next will be Lim, whom he suffered a stunning defeat to in the first round of the 2021 event.
The Singapore player, aged 71, became the oldest player to win a World Championship match after a 3-1 triumph over Jeffrey de Graaf.
Backed by a raucous and partisan Ally Pally crowd, Lim snagged the opening set while riding a 94.86 average.
It prompted a response from opponent De Graaf, whose 108 checkout pushed him to level the match.
The turning point came in a last-leg decider in set three when De Graaf busted his 70 score on double 16 instead of eight, allowing Lim to swoop in and erase 71.
A shaky fourth set was taken all the way to another decider, where 'The Singapore Slinger' prevailed, removing 56 on tops to send the crowd into raptures.
"First and foremost, I'm thankful to be here, and I'm thankful to this crowd behind me," a grateful Lim told Sky Sports. "Just to make it here is an achievement.
"No matter how good you are, there are times when you can miss a shot, and you've just got to take advantage.
"I just took the advantage, and I'm glad."
Meanwhile, rising star Wessel Nijman lost just three legs to cruise past Karel Sedlacek 3-0 in a performance averaging a tick over 100.
A 136 checkout headlined a first set which saw Dutchman Nijman average 111.17, platforming the 25-year-old for the rest of the contest.
He edged a back-and-forth second stanza before completing a routine win in just over 20 minutes.
Nijman will face former semi-finalist Gabriel Clemens in the next round after a dominant 3-0 showing against American Alex Spellman to end the night.
Germany's Clemens reeled in the 'Big Fish' 170 checkout in the first set and never looked back, winning nine of 10 legs played.