The world number 49 from Wallsend beat White 4-1, sealing his victory with a 104 break in frame five.
"I'm just happy to get the result," the 30-year-old told BBC Newcastle.
"It was a case of - for my own self-confidence - trying to put on a bit of a performance and trying to get through with a couple of decent breaks."
Wilson, known as the Tyneside Terror, has failed to progress past the third round at any event this season said he was encouraged by his form.
"The last couple of months in practice I feel like I've been playing well. I feel like I've been at ease with my game which has been a struggle for me a lot of the time," he added.
"Some tournaments I've done quite well in and I've still not even been happy inside - I've been getting away with the odd thing and just getting by on my ability.
"But I feel like I'm in a good position at the minute and I'm just hoping I can kick on and actually start performing in the matches now."
Wilson faces Chinese world number 16 Liang Wenbo in the second round on Tuesday and insists he will not be deterred by his opponent who is known for his exuberance around the table.
"It's not so much off-putting but I do sometimes sit there with a smile on my face because he's a great character," he said.
"It's good for the game really but it doesn't put me off or anything."
Gary Wilson says he feels at ease with his game after knocking six-time World Championship finalist Jimmy White out in the first round of the Welsh Open.