Defender Rob Atkinson headed in from a corner before Danny Boshell secured all three points after beating the offside trap and flicking the ball over Kevin Pilkington.
Newell said: "At this stage of the season it's just vitally important we keep winning and although it wasn't pretty football, a win is still a win.
"In this day and age it's impossible to keep the result from the lads so when we kicked off we knew Chester had already beaten Accrington and we knew what we had to do.
"Our performance in the first half was poor, but our defending and goalkeeper kept us in it. Henderson pulled off some cracking stops and that allowed us a base from which to play some football in the second half.
"We didn't let them settle on the ball after the break and Boshell's goal sealed it for us. We knew he was onside, even if Adrian Forbes wasn't, but I'm glad the officials got it right in the end."