The Steelmen took advantage of some mediocre Saints bowling to amass 257 for five declared after being put into bat at Elwy Park.
Asaph's leading bowler was Matthew Hulse with four for 70.
The hosts had to bat out 61 overs to avoid defeat and they so nearly did so, Matt Naylor the last man out off the fourth ball of the final over of the match.
Asaph finished 160 all out, skipper Richard Aram striking a battling 68, Johnny de Bartolo 30 and Gareth Jones a swashbuckling 24.
The defeat leaves Saints 15 points adrift at the bottom with seven matches to save their skins.
nSt Asaph 2nds remain bottom of division two following a nine-wicket defeat at Pwllheli. The visitors set 107 for nine with only Colin Fleming (24) making any real impact. Pwllheli replied with 110 for one to scoop a 9-1 success.
nAbergele were on the wrong end of a draw at Dolgellau where home opener Phil Leeds hit 105 not out to take his team to 174 for four with only Phil Moulson (two for 45) having any real success with the ball.
Abergele soon lost early wickets and it was left to Grahm Price (26 not out) and Dewi Davies (18 not out) to see Abergele to 112 for seven.
nAbergele second team were shot out for 86 by Connah's Quay who knocked off the winning runs for the loss of five wickets.