Part lost the opening five legs but recovered to win 2-1 after being a set down, with Lewis missing three darts for the match in the second set.
Vincent van der Voort also won by the same scoreline, only dropping one leg in his defeat of Kevin Painter. The Dutchman will face Wade in the second round.
Brendan Dolan beat Wayne Jones 2-0 to record his first Grand Prix victory since 2004 but his Irish compatriot William O'Connor lost to Andy Smith in the final contest of the night.
There were also victories for John Henderson - who beat Justin Pipe 2-0 - and Wes Newton, who came from behind to beat former world number one Colin Lloyd.