Kris Holt and Jude Smith were the heroes for the Cutters as Holt collected a brace, and Smith saved a late penalty to keep Daisy Hill in the lead.
Despite being second best for the much of the match Daisy managed to get over the line which left manager Nicky Hunt encouraged.
"I said to the lads at the end the pleasing thing is, they found a way to win when they were under pressure.
“We were under the cosh for the last 15-20 minutes of that game, and the lads have shown a different type of character, a different side to them, but they've got to carry that on now.
“Obviously with Jude saving a penalty late on, it just gave everyone the massive lift that we needed to see out the last five or six minutes of the game.
“Squires Gate won't be in the bottom four or five this season. They've got a really good manager, a good work ethic and some really good players, and you've got to give credit to them.
“They put us under an enormous amount of pressure and that's probably the first time since I've been in with my team here, that we have been under that amount of pressure. We have dictated a large number of games that we've played recently, but not today.
“In general, over the 90 minutes, we were second best for winning every second ball, and that's not like us. In the past few weeks, we've been on the front foot, but we just couldn't get our rhythm today.
“But I've seen a different side to us today. We needed to dig in and we saw the game out.
“Maybe Squires Gate will say they deserved a point at least, and they probably did, but sometimes you don't get all you deserve in football”.
A fast start for Daisy nearly resulted in a goal 3 minutes in as Liam Sheppard raced down the wing and whipped in a delightful cross for Kaiden Barlow but he headed just wide of the post.
Twelve minutes in and Daisy did get the opener as Kris Holt poked home. Barlow recovered Joleon Moore’s cross and laid it off for Holt on the corner of the 6-yard box where he managed to get just enough on the shot to squirm under Joel Sargeant.
Squires Gate looked for a response from a corner routine which found Ben Thomas free at the edge of the box but his strike from 25 yards went over Jude Smith’s goal.
Only two minutes later Squires Gate did get their equaliser as Dean Ing acrobatically volleyed Kevin Zokou’s cross into the bottom corner.
Holt nearly found himself on the score sheet again as he connected with Declan Baldwin’s freekick only to head over from just outside the 6-yard box 38 minutes in.
Five minutes later Holt finally secured his brace as he scored a near identical goal as his first. Jacob Ridnings whipped a cross in that Ntumba Massanka managed to keep in on the byline and set it for Holt who stabbed home from the edge of the 6-yard box to put Daisy ahead going into half time.
Smith was forced into a superb save 67 minutes in as Fin Lynch fired a low cross in for Ing whose shot from around the penalty spot looked destined to nestle in the goal until Smith flew along his goal line to keep out the strike.
With 82 minutes gone Daisy conceded a penalty as Fionn Murphy brought down Scott Harries just inside the area.
Ing stepped up and struck the ball to the bottom right, but Smith guessed correctly and got down quick to save before the rebound was cleared.
In the first minute of added time Squires Gate had their final chance to level the encounter as a long throw caused havoc and fell for Will Squires, but he volleyed his effort wide of the far post.
Daisy are back in action on Monday when they host Colne at the Ginge Power Stadium in the North West Counties First Division North (7.45pm).