Left-back Johnny Hunt scored the first goal of the new National League campaign inside five minutes to give the Blues the best possible start, but it was heavy going from then on.
Braintree worked hard without the ball to prevent the hosts from settling into the game and had the lion’s share of possession, although lacked the quality to turn that into genuine chances with Ben Heneghan and Ian Sharps marshalling the back four well.
Over the course of the season, Chester will produce much better performances than this and not win, so Burr was understandably delighted to get three points on the board.
"I think there was a lot of anxiety in our play compared to how we were in pre-season but you’ve got to give credit to Braintree," said Burr.
"Without actually hurting us, they knocked it about well and have got good movement. We just had one of them days where we had to dig in and get the result.
"Probably looking at this time last year, we’d have maybe not won that game.
"At the back the boys were immense but you defend from the front and the lads have put a good shift in so I’m really pleased."
IN PICTURES: Action from Chester FC's 1-0 win over Braintree Town
Hunt provided the best moment of the match on four minutes, picking up a short corner and darting into the box before curling his shot around keeper Will Norris.
Norris had a quieter afternoon than he might have expected between the sticks, although the woodwork came to his rescue twice in the second-half with Jordan Chapell and John Rooney seeing shots crash against the uprights.
"We’ve been working on a few set pieces this week and I thought John took it really well,” said Burr of the winning goal.
"The start that we had, I was hoping we’d go on and really dominate but it was one of those games where we couldn’t get going or get ourselves into top gear. It’s pleasing sometimes to win a game when you’ve not played as well as you would have like to have played.
"We know how tough the season is going to be again and it’s great to be off to a winning start. We’ve got a good group of lads and it was one of those days where picking the team and getting the bench right was important, and obviously with the win it’s proved that we did the right thing.
"We tried to inject the subs to make a difference but couldn’t seem to get out of that fourth gear. You get games like that and I was just so pleased to see a team of mine win where we contained whatever Braintree threw at us."
Chester travel to the Pennines on Tuesday night to face FC Halifax Town (7.45pm) with Shaymen boss Neil Aspin and his side looking to bounce back from a disappointing 3-1 defeat at newcomers Boreham Wood on the weekend.