Day Eight of the £2.5million event featured a star-studded cast at the Alexandra Palace, and two-time World Champion Anderson marked his 52nd birthday with a hard-fought win over Madars Razma.
Anderson - who boasts more wins on the Alexandra Palace stage than any other player - came through a high-quality opening set with a 105 average, courtesy of 12, 15 and 13-dart legs.
Razma responded with 121 and 134 finishes in consecutive legs to restore parity, and a superb 154 checkout midway through set three gave the Latvian the opportunity to throw for a 2-1 advantage.
However, Razma squandered four darts at double for the set and paid the price, as Anderson conjured up 121 and 110 combinations in the latter stages to wrap up a 3-1 success.
"This is every dart player's dream just to stand on this stage," said the Scot, who is one win away from registering a half-century of victories at the PDC World Championship.
"Even me - if I cannot smile coming here - this is the place that you need to be. It's just a great atmosphere and a great place for the World Championship.
"I'm not sure if I can win it this year. My game is not even close to what it should be, but I keep trying, and I am practising a lot more."
However, while Anderson preserved his bid for a third World Championship crown, Wade became the biggest name to exit this year's tournament, following a dramatic deciding-set defeat to Williams.
Wade made an assured start, winning the opening set with a flawless display of finishing and kicking off set two with a 107 combination, only for Williams to reply with six straight legs to storm into a 2-1 lead.
Wade - a four-time semi-finalist in the sport's showpiece event - responded by completing a clean sweep in set four, taking out an 84 kill to level the tie as the pendulum continued to shift.
Williams was undeterred however, following up a clutch 66 finish with a 13-dart hold to 2-1 ahead in set five, and a fourth 180 propelled the Welshman to a landmark victory.
"It's one of the biggest wins of my career," admitted Williams, who won his maiden PDC title at a Players Championship event back in March.
Thursday December 22, afternoon session
- Krzysztof Ratajski 3-1 Danny Jansen (3-1, 0-3, 3-1, 3-1)
- Ryan Searle 3-0 Adam Gawlas (3-2, 3-1, 3-0)
- Mensur Suljovic 3-0 Mike De Decker (3-1, 3-2, 3-1)
- Dirk van Duijvenbode 3-2 Karel Sedlacek (3-1,1-3, 2-3, 3-1, 4-2)
"It was a tough game. I think it was tough for James as well, it's his first game and he's a fantastic player. I think I tried a bit too hard, but I dragged it out of myself at the end."
Elsewhere, fifth seed Humphries also survived a scare to set up an explosive third round tie against Vincent van der Voort, after edging out Germany's Florian Hempel in a five-set tussle.
Hempel, who defeated the-then fifth seed Dimitri Van den Bergh at this event 12 months ago, threatened to repeat the feat after claiming a scrappy opening set.
Humphries fired in back-to-back 12-darters in set two to draw level, and while Hempel edged back ahead, the Berkshire star produced another clean sweep in the fourth to send the match all the way.
The pair traded holds to kick off the fifth set, but after wiring the bull for a spectacular 170 outshot, Humphries returned to break via double eight, and then pinned the same target to complete the comeback.
"I played well in patches. Florian played well when I played well, and played badly when I played badly. It was a strange game," reflected Humphries, who landed seven 180s to advance.
- Gary Anderson 3-1 Madars Razma (3-2, 2-3, 3-2, 3-2)
- Jim Williams 3-2 James Wade (1-3, 3-1, 3-0, 0-3, 3-1)
- Luke Humphries 3-2 Florian Hempel (2-3, 3-0, 1-3, 3-0, 3-1)
- Vincent van der Voort 3-0 Cameron Menzies (3-0, 3-1, 3-2)
"I showed my resilience there and I think the experience I've gained over the last 18 months has allowed me win that game.
"I've got a different mindset now. You don't get to number five in the world by throwing in the towel and I worked hard to get over the line there, even though I wasn't at my best."
Humphries will now play two-time quarter-finalist Van der Voort for a place in the last 16, after the popular Dutchman raced to a 3-0 win over debutant Cameron Menzies.
Van der Voort averaged almost 105 to clinch the opening set in style, and after taking out a crucial 121 finish en route to a 2-0 lead, he capitalised on Menzies' outer ring woes to seal a straight sets win.
Earlier in the day, Van der Voort's compatriot Van Duijvenbode came through the first tie-break of this year's tournament, crashing in an incredible 12 maximums to edge out Karel Sedlacek in a five-set thriller.
Van Duijvenbode stormed to the opening set with a 108 average, and although an unfazed Sedlacek hit back to establish a 2-1 cushion, the three-time TV finalist responded to level at two apiece.
Friday December 23, Afternoon session
- Brendan Dolan v Jimmy Hendriks
- Chris Dobey v Martijn Kleermaker
- Ross Smith v Darius Labanauskas
- Rob Cross v Scott Williams
The Dutchman then produced a blistering barrage in set five, and despite landing six 180s and missing double 12 for a nine-darter, he was forced to survive a match dart at bull before sealing his progress.
"I have never felt this nervous in my life," revealed Van Duijvenbode, who landed 11 perfect darts during a magical spell in the closing stages.
"I think it's because I think I can actually do something this year. I started well and then the pressure kicks in, but in the end I won, so I'm happy."
Elsewhere, Ryan Searle eased through to a third round showdown against Jose de Sousa, producing a fine display of finishing to dispatch Czech youngster Adam Gawlas in straight sets.
Searle drew first blood with 100, 94 and 80 checkouts before punishing Gawlas' doubling woes to open up a two-set cushion, and he wrapped up victory with a clinical two-dart 98 combination.
Mensur Suljovic also advanced to the third round with a 3-0 success, punishing a profligate display from Mike De Decker to set up a clash against three-time World Champion Michael van Gerwen.
- Martin Schindler v Martin Lukeman
- Danny Noppert v David Cameron
- Jonny Clayton v Danny van Trijp
- Joe Cullen v Ricky Evans
Meanwhile, in the afternoon's curtain-raiser, Krzysztof Ratajski recorded a battling 3-1 win over Dutch debutant Danny Jansen to book a showdown with Belgian number one Dimitri Van den Bergh.
The second round draws to a close on Friday at the Cazoo World Darts Championship, with 2018 winner Rob Cross in action, alongside Jonny Clayton, Danny Noppert and Joe Cullen.
The Cazoo World Darts Championship is being broadcast live on Sky Sports in the UK & Ireland, through the PDC's worldwide broadcast partners including DAZN and Viaplay, and on PDCTV (excluding UK, Ireland, Germany, Austria & Switzerland based subscribers).