Davis admitted reaching the second round felt like "climbing a mountain," and claimed the effort involved amounted to "torture" at the Crucible Theatre, Sheffield.
The 52-year-old has some way to go before matching the feat of the late Australian Eddie Charlton who, at the age of 59 beat Cliff Thorburn in the first round in 1989 – the year Davis landed the last of his six world titles. Davis last night ousted his friend Mark King 10-9 in a match which concluded as midnight loomed.
The Romford pair fought a terrific match which went right down to the final pink. King, 36, potted it unintentionally when he needed a snooker, and there was no way back.
Higgins will have been pleased by the outcome, having indicated a desire to face his childhood snooker hero.
"Considering I haven't played much competitive snooker, that was like climbing a mountain for me," Davis said later.
Title favourite Ronnie O'Sullivan withstood a fightback from Liang Wenbo to win 10-7.