White, 60, made his first appearance in the final stages of the tournament in over a decade after beating former winner Stephen Maguire and world number 57 Dominic Dale in qualifying to reach the last 32.
After losing two close opening frames to the world number 16, White faced an uphill task, but responded by taking the third frame with a break of 55.
Day regained his two-frame advantage with a brilliant score of 127 and another century break (105) in the sixth frame saw him open up a 5-1 lead.
White took the seventh frame to the delight of the Barbican crowd, but Day wrapped up his victory with a break of 63 in the eighth.
Day will play Sam Craigie in the second round after the 28-year-old from Newcastle knocked out defending champion Zhao Xintong 6-2 earlier on Saturday.
Zhao, 25, who beat Luca Brecel in last year's final, led 2-1 but was made to pay for several key mistakes by world number 47 Craigie, who had opened the match with a frame-winning break of 83.
Craigie made scores of 78 and 69 to lead 3-2 ahead and sealed one of the best wins of his career with a break of 104.
Northern Ireland's Mark Allen overcame fellow countryman Jordan Brown 6-4 to set up a second-round tie against Kyren Wilson, who defeated Matthew Selt 6-3.
World number nine Allen, the Northern Ireland Open champion, trailed 2-0 but recovered to win five of the next six frames with breaks of 68, 105, 113, 63 and 55.
Wilson, the world number seven, stormed into a 2-0 lead after opening breaks of 103 and 101 and sealed victory with a score of 74 in the ninth frame.