Ace cueist Advani scored total of 266 points, which helped him to grab straight four frames in the best of seven frames game, while Slessor was restricted to 31 points.
The 30-year-old will face the winner of the match between Stephen Maguire and Alfie Burden in round two tomorrow.
Earlier in the Wild Card round, Advani defeated world number 109 Fang Xiongman 4-2 yesterday.
In another match, Ishpreet Chadha lost to Dominic Dale 2-4 and failed to qualify for the second round.
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