The Welshman surged into a two-frame lead, with an opening break of 120 offering few reasons for concern.
Williams pulls off World Open comeback to win title
But Kleckers, ranked 103 places lower than his opponent in the world rankings, produced a three-frame run before moving within a frame of victory thanks to a break off 66 in the seventh frame.
Faced with the prospect of exiting the competition at the first hurdle, Williams required two quality frames, and that's exactly what he produced.
Breaks of 94 and 77 saw the world champion avoid the upset and remain in the competition.
Ding Junhui also survived a scare before overcoming James Wattana 4-3.
The former world number one let a 3-1 lead slip as his 48-year-old opponent reeled off breaks of 59, 54 and 102 to move within a frame of victory.
However, Ding steadied to book his place in the main draw - drawing level at 4-4 before sealing victory with a knock of 80 in the ninth frame.
World Open Results
- Ding Junhui 5-4 James Wattana
- James Cahill 5-1 Liang Wenbo
- Neil Robertson 5-0 He Guoqiang
- Yan Bingtao 5-3 Ashley Carty
- Mike Dunn 5-0 Luo Zetao
- Ben Woollaston 5-1 Bai Langning
- Chang Bingyu 4-5 Jimmy Robertson
- Mark Williams 5-4 Lukas Kleckers
- Robert Milkins 5-4 David Lilley
- Marco Fu 5-4 Peter Ebdon
- Ali Carter 5-0 Rory McLeod
- Ricky Walden 5-3 Dominic Dale
- Barry Hawkins 5-2 Jimmy Robertson
- Matthew Selt 5-4 Lee Walker
- Fergal O'Brien 5-4 Zhao Xintong
- Luca Brecel 5-4 Scott Donaldson
- Gary Wilson 5-3 Tom Ford
- Jamie Jones 5-2 Zhou Yuelong
- Ryan Day 5-2 Robbie Williams
- Noppon Saengkham 5-3 Rod Lawler
- Jak Jones 5-3 Zhang Anda
- Jack Lisowski 5-0 Chris Wakelin
- Stephen Maguire 5-4 Thepchaiya Un-Nooh
Willams produces stunning comeback to reach semi-finals