The world number one and three-times world champion will face Jamie Jones in the last 32 after the Welsh world number 39 completed a 5-2 victory over Zhou Yuelong.
Former UK champion Judd Trump was more convincing in his first-round victory, emerging with a 5-1 win over world number 67 Martin O'Donnell courtesy of breaks of 54, 84, 54 and 73.
Williams pulls off World Open comeback to win title
O'Donnell contributed 54 and 55, but was powerless to prevent world number five Trump from securing a meeting with Gary Wilson in the last 32.
Slessor, who reached the Northern Ireland Open semi-finals before losing to world champion Mark Williams last November, certainly proved a tough assignment for Selby, who saw the Gateshead player level at 3-3 from 3-1 behind.
Selby - who lost the final of this event to Shaun Murphy in Haikou four years ago - claimed two frames on the black for a 3-1 lead with Slessor winning the third frame courtesy of a break of 62 boosted by a late fluke on the blue.
It was the first time Slessor has won a frame against Selby having suffered a 4-0 defeat at the Paul Hunter Classic and a 5-0 loss at the China Open over the past few years.
Slessor - ranked a rising 44 on the one-year ranking list - pinched the fifth frame before a run of 105 saw him restore parity at 3-3.
Selby then produced a 62 in the seventh frame, his highest break of the match, and timely enough to move one up with only a possible two to play.
Despite recovering three snookers in the penultimate frame, the doughty Slessor missed a brown needing the four remaining colours as Selby finally dragged himself over the line to reach the last 32 when a re-spotted black looked likely.
Not at his best, but certainly effective enough in the end.
Yushan World Open Round One results
- Mark Selby 5-3 Elliot Slessor
- Mei Xiwen 5-2 Simon Lichtenberg
- Neil Robertson 5-1 Andy Lee
- Judd Trump 5-1 Martin O'Donnell
- Andrew Higginson 5-4 James Cahill
- Anthony Hamilton 5-2 Mark Joyce
- Mark Williams 5-1 Alexander Ursenbacher
- Harvey Chandler 5-4 Kurt Maflin
- Yan Bingtao 5-0 Stuart Carrington
- Kyren Wilson 5-1 Paul Davison
- Mark Allen 5-1 Lu Haotian
- Ben Woollaston 5-1 Chang Bingyu
- Xiao Guodong 5-1 Michael Georgiou
- Joe Perry 5-4 Mike Dunn
- Ding Junhui 5-3 Yuan Sijun
Willams produces stunning comeback to reach semi-finals