The Thanet Road club are 15 points behind leaders Featherstone with two games to go and the top two clash in the final game of the season on March 2.
York got off to a good start against Selby, leading 22-13 after five ends and 41-26 after ten.
At home, Dave Stroughair’s team led 14-3 after nine ends before Sam Arundale’s side won seven of the last eight ends to only go down 22-13.
Phil Emmerson’s side trailed 5-4 to John Phillips’s team after three ends before a good run made the score 20-7 to the home side and it finished 27-16.
In Selby, Paul Humphreys’ team held on to win 14-13, while Dave Attwood’s rink won the last five ends to beat Roger Wood’s side 17-12.
New Earswick’s hopes of going straight back into division one all-but disappeared when they lost to division two leaders Hornsea, who moved 31 points ahead of their rivals.
The game was close up to the 18th end when the aggregate score stood at 66-63, but Hornsea pulled away to win 78-69.
At home, Paul Dawson’s side led 12-4 after ten ends and held on to win 18-17, while Barry Harrison’s team won 22-16.
Away, Brian Gray’s team went down 20-12, while Bill Waldie’s team dropped nine shots between the tenth and 15th ends in a 25-17 defeat.