Day's defeated; sport ROUND-UP.
Hastings cueman Davis had only reached the second round once previously, when he lost to Peter Ebdon in 1995, but claimed a 10-8 win over Day.
He will face Northern Ireland's Mark Allen in the second round in Sheffield.
Day followed fellow seeds Mark King and Marco Fu in making a first-round exit.
Earlier Ding Junhui made short work of wrapping up a 10-1 victory over Stuart Pettman.
Australian Neil Robertson made sure of his last-16 place after a gruelling final session in his match against Ireland's Fergal O'Brien, winning 10-5.