Dutch icon Van Barneveld, a crowd favourite at AFAS Live, dominated his match against Johan Engstrom, winning 6-0.
Meanwhile, Littler survived a match-deciding leg to edge out Ross Smith 6-5.
Saturday's highly anticipated second-round clash between Van Barneveld and Littler promises to be a thrilling rematch of their 2023/24 World Championship encounter.
Littler - famously a huge fan of 'Barney' as a young child - emerged victorious in that match, and Van Barneveld will be eager to reverse the result in front of a passionate Amsterdam crowd.
Van Barneveld's performance on Friday was nothing short of exceptional, landing three 180s and limiting Engstrom to just two double attempts.
After the match, Van Barneveld expressed his gratitude for the home crowd's support and acknowledged the challenge posed by Littler:
"The crowd are always backing me because in their mind, I'm a legend - but you still need to do it," Van Barneveld told the PDC website.
"You have to rely on yourself and take your chances and keep on putting him under pressure all the time.
"Playing for your home crowd is fantastic, but tomorrow you play a guy who can play like Phil Taylor! He's fantastic - I'm really looking forward to it.
"I know what I need to do to beat him; to play my A-game and maybe even more than my A-game. If you play well you always get chances, but you have to take them."
Littler's victory over Smith was a hard-fought battle that went down to the wire.
The teenage sensation averaged 103.3 but had to fight back from a 5-3 deficit to force a deciding leg. He eventually clinched the match with a trademark double ten finish.
"I'm glad to get over the line," admitted Littler. "Ross let me in and I took my chance.
"Me and Raymond will both be confident and I'll go into the game wanting to win, just like tonight.
"I'll just play my darts - in the worst case I'll have to switch on the gears again like I did tonight, but I'll have to try to get off to a good start tomorrow."
Other notable first-round results included Michael van Gerwen's 6-4 win over Jonny Clayton and Danny Noppert's 6-3 victory over Gian van Veen. Van Gerwen will now face Noppert in a rematch of the 2019 final.
The second round of the Jack's World Series of Darts Finals takes place on Saturday evening, with the tournament culminating in the final on Sunday.