The St Leonards cueman is 4-3 up against Chinese world number three Ding Junhui at The Crucible in Sheffield. The game will be played to a finish from 10am tomorrow.
Nine frames were scheduled for the opening session, which started shortly after 2.30pm, but only seven were possible before the players had to vacate the arena in time for the 7pm matches to take place.
Things looked like being even better for Davis as he won all of the first four frames. The world number 18 came through a scrappy opener on the pink before edging an equally tight second frame.
502 Bad Gateway
A break of 66 paved the way for Davis to clinch frame three, and he proceeded to win frame four as well courtesy of a 56 break and 20 points in fouls.
Ding upped his game after the interval, though, and runs of 66, 109 and 76 gave him the next three frames to reduce his deficit to one.
Davis had to win three best-of-19 matches at the qualifiers just to get to The Crucible. The 42-year-old saw off Joe O’Connor 10-4, Oliver Lines 10-7 and former world champion Ken Doherty 10-3.