Littler took to the Alexandra Palace stage for the first time in this year's event on Saturday night, beginning his quest as one of the favourites to take home the London major.
But it was far from plain sailing for the teenager, who was made to work by Meikle in the first three sets of the match.
Despite his sluggish start, 'The Nuke' exploded in a record-breaking fourth set which saw him average 140.91 and nearly hit a nine-darter after narrowly missing double 12.
Following the 3-1 victory, an emotional Littler could only manage a few words during his interview with Sky Sports, which did not restart as he left the arena after embracing his parents.
Littler later put his post-match tears down to nerves and suggested it was "probably the toughest game" he has played in his career so far.
"That was probably the toughest game I've ever played, but you've got to get over the line," Littler said.
"I don't know where I pulled that last set from, but I just had to fight until the end."
Explaining his emotions, he added: "When I got on that stage I felt really nervous, but I managed to find my game from somewhere.
"I know I am the favourite, but you have to focus on winning your first game, and that's what I did tonight."
Littler's progression ensures he will return to Ally Pally after Christmas in the third round to play one of Ritchie Edhouse or Ian White.