The two Englishmen faced off in the final match of Monday's afternoon session at Alexandra Palace, with the pair battling it out to a full five sets in a thrilling encounter.
Wade won the first before being pegged back twice by Evans, only to bounce back to tie the score at 2-2 heading into the decider.
There was very little to separate the pair in the final legs of the match, with one player needing to win by two clear legs to advance.
Both missed several match darts, with Evans eventually coming out on top after hitting 99 to check out and seal a 6-4 win in the final set.
Elsewhere, fan favourite and Ally Pally cult hero David Munyua exited the tournament after a 3-0 defeat at the hands of Kevin Doets.
Munyua captured the hearts of supporters with his spectacular comeback against Mike De Decker in the opening round but came undone against Doets, winning just two legs across three sets.
The world number 40 booked his spot in the third round with an emphatic victory, averaging 90.12 with five 180s thrown.
"I tried my best, but Doets was much better than me. He played a good game, (better) than I could," Munyua told the PDC after his defeat.
"I wish him the best.
"With it being my first time at Ally Pally, I've done my best and I'm happy with that."
Clemens and Razma advance
Earlier in the afternoon session, German player Gabriel Clemens picked up a 3-0 victory over Wessel Nijman, coming from one leg down in the first and third sets to advance to the third round.
He will face either former champion Luke Humphries or Paul Lim, who face off in Monday evening's session.
Latvia's Madars Razma also booked his spot in the third round after a 3-1 triumph over Scotland's Darren Beveridge.
It took some doing from Razma, who battled back from two legs down in the fourth set to clinch victory and put an end to what would have been a dramatic comeback from Beveridge.
He will now face either Gian van Veen or another Scottish player in Alan Soutar - who go head-to-head on Monday evening.
Monday's 2026 PDC World Darts Championship results
Afternoon session
Darren Beveridge 1-3 Madars Razma
Wessel Nijman 0-3 Gabriel Clemens