Having not won in the league since December 19 and picked up only six points from their previous 10 league games, the Blues had fallen down the National League table at an alarming rate.
Defeat at Moss Lane would have seen them drop below Altrincham to 19th, however the Blues put recent disappointments behind them with an excellent display.
Danny O'Brien gave them a deserved lead on 26 minutes on his debut and Ryan Astles made it 2-0 on the stroke of half-time before Ross Hannah's 18th goal of the season in the 76th minute secured a much-needed three points.
"It's been a long coming hasn't it and it's been really frustrating but I'm really pleased with not just getting the three points, that was the main thing, but the way we went about it," said Burr, who made five changes in an attacking side with first starts for O'Brien, Sam Hughes and Tony Thompson in goal.
"I've looked at the games we've got coming up and from now to the end of the season the points that are available and realistically the points that we can pick up and I felt that this was a game we needed to attack from the start and you've seen that from the line-up.
"It's what we needed. It's give the lads a big boost and it was a good team performance, a hardworking performance but with some good football as well.
"The people I'm most pleased for tonight are the supporters because again they've come in good numbers on a miserable night and we've not give them much to shout about over the last few weeks and months but we're trying to get ourselves back on track and I'm pleased for them."
Chester could have taken a 3-0 lead a minute into the second-half when the outstanding Jordan Chapell tore through Altrincham's defence and rounded keeper Tim Deasy before Marcus Holness pulled him to the ground for a stonewall penalty.
Hannah took the spot-kick but blazed his effort well over the crossbar, however the striker later made amends with a poacher's finish for the third goal.
"I thought he was putting me through the mill a little bit when he missed the penalty," Burr said.
"We spoke at half-time about kicking on and going on to get more goals because one back for Alty could have been a bit shaky for us with the form we've been in.
"We got the penalty straight after half-time and I'm thinking 'right, great 3-0 we can enjoy this now' and he's gone and missed it but it's just one of those things.
"We've gone with the three centre halves and played two wingers as well and everything's worked out and it's always pleasing when you've worked on things in the week leading up to the game and you get the right result.
"Before I arrived at Chester there weren't many occasions where I lost to Alty but I must say the times that we've played them this season and last season they've always done well against us and they've been a bit of a bogey side but I think we've put that well to rest."