The 58-year-old, who has slipped to 100 in the world rankings, failed to make a half-century break at Ponds Forge.
China's Ding Junhui defeated Ireland's Greg Casey 10-4, while compatriot Liang Wenbo beat England's Joe O'Connor 10-2.
There are three rounds of qualifying, with 16 qualifiers joining the world's top 16 at the Crucible from 16 April.
Davis' last appearance at the Crucible showpiece came in 2010, when he produced a surprise run to the quarter-finals before being beaten by eventual champion Neil Robertson.
Ding, an 11-time ranking event winner, is playing the qualifiers for the first time since 2007 after a disappointing season that has seen him drop out of the top 16.
Two-time Crucible finalist Ali Carter is also through to the next stage of qualifying.

The pages from a 13th Century text of the holy book of Islam were purchased by the council in 1951.
Conservator Richard Hawkes said: "This is the earliest example of paper that I have worked on."
Leeds City Council said the paper's age and origin were confirmed by the Victoria and Albert Museum in 2014.
The pages mainly show surahs (or chapters) 29 and 30, said the council.
Councillor Brian Selby said: "The painstaking work of the museum team has ensured the pages can be displayed in a way which fully captures their significance as well as how ornate and beautiful they are."
Leeds City Museum's display starts on Saturday and is to run for a year.
Six-time champion Steve Davis failed to reach the World Championship as he lost 10-4 to Fergal O'Brien in the first round of qualifying in Sheffield.
[NEXT_CONCEPT]
Two pages from an 800-year-old copy of the Koran decorated with gold leaf are to go on show in a Leeds museum display looking at Islam.