Adam Dugdale's late strike eased the pressure on boss Steve Davies to earn Crewe a rare win.
Alex have only won three games this season, but Davies's players stood up to be counted in a dire game.
Dugdale netted his first of the campaign in the 84th minute.
Fellow central defender George Ray nodded down a corner from substitute Billy Waters and Dugdale was first to react to belt the ball in from a couple of yards.
Relieved boss Davies joked:
"That's back-to-back wins - it's unknown!
"We're not going to go from one performance to the next in giant leaps, it'll be little strides. It wasn't a great spectacle, but we were slightly better and just nicked it."
Walsall striker Jordan Cook should have put his team ahead in the 69th minute minutes, but nodded a cross from Andy Forde straight at keeper Ben Garrett with the goal begging.
Garrett then played a big part in the win six minutes later when he back-peddled furiously to tip over a cheeky lob from Cook.
Former Saddler Febian Brandy came closest to breaking the deadlock before the break.
In the 24th minute Brandy picked up a pass from skipper Matt Tootle on the right side of the box and his fierce shot was fumbled by keeper Richard O'Donnell who recovered to fall on the ball before it trickled into the net.
And Walsall's best effort of the half fell to left back Andy Taylor, but his 25 yard screamer took a deflection off team mate Cook and flew inches wide.
Disappointed Saddlers manager Dean Smith saw his team slip into the drop zone and said:
"We didn't really show a lot of desire to get the ball into the back of the net. We lacked a little bit of nous."
Romaine Sawyers stunned league leaders City with a late equaliser, but their unbeaten start to the season continued.
Striker Sawyers played a one-two on the edge of the box with winger Andy Forde before curling a side-foot stunner into the top corner for his second goal of the campaign before flying to Haiti to for a St. Kitts and Nevis Caribbean Cup game.
And Bristol City boss Steve Cotterill praised Sawyers goal. He said:
"You have to take your hat off at times. That was a wonderful finished. All in all, it was a fair result. We're still unbeaten and I've told the players to be proud of that.
Joe Bryan had the Robins rocking though with his first league goal of the season in the eleventh minute.
Central defender Luke Ayling picked Bryan out with a cross field pass and the winger cut into the box from the left flank before drilling a low fourteen yard shot past helpless keeper Richard O'Donnell.
Walsall started the game brightly and defender Andy Butler hooked a volley into the arms of keeper Frank Fielding in the first minute.
Five minutes after Bryan's opener, central defender Paul Downing nearly gifted City a second.
Downing dithered on the edge of his box and striker Aaron Wilbraham nicked the ball off his toes, but fired a low shot straight at O'Donnell.
But Fielding needed to be at his best in the 25th minute to touch a twenty yard curling shot from Forde just over the bar.
Saddlers manager Dean Smith was delighted with his side, but said:
"I thought we deserved more if I'm honest. We were disappointed with their goal, but think we have a goal of the season contender and I thought we had them on the back foot in the second half."
Wes Burns scored a last gasp winner to stun the Spireites as leaders City kept their super start going.
First half substitute Burns lashed home his first of the campaign from ten yards after meeting skipper Wade Elliott's 93rd minute right wing cross to make it eight wins from twelve games.
City are now five points clear at the top and delighted boss Steve Cotterill said:
"They had some good possession and played some good football, take nothing away from them.
"I was delighted that Wes Burns got the winner because he's made the mistake for their second when he hasn't gone with the runner and they've played a one-two around him, but that's what you'll get from young players. Two of our young players have given the ball away in the final third, but that's what happens with young players, bless 'em. Hopefully they'll be better for their experiences.
"I've been dying to get to 3-4-3 at the right time and today I thought right, let's have a go at it. We got to it, albeit for six minutes, and thankfully that got us the winner.
"It's always a test of character and team spirit when you go goals up and they peg you back.
"Late in the game we got enough bodies in the box looking for the winner which is pleasing."
Spireites skipper Ian Evatt inadvertently opened the scoring for City in the ninth minute.
Defender Tendayi Darikwa lost the ball on the edge of his own box and hapless central defender Evatt turned a low cross from left winger Joe Bryan into his own net from two yards out at the near post.
Bryan then turned villain for Chesterfield's 25th minute leveller when he also gave the ball away just before Eoin Doyle was bundled over by full back Derek Williams in the box.
Striker Doyle then picked himself up to from the spot.
Left back Williams then made amends to put City ahead again less than one minute after the break.
Winger Luke Freeman floated over a corner from the right right wing corner to the back post and Williams nodded His first of the season back into the far corner.
But Doyle kept his amazing hot streak going when he tapped in his FIFTEENTH of the season from two yards in the 59th minute after co-striker Sam Clucas mishit Darikwa's teasing Low cross.
Chesterfield manager Paul Cook remained upbeat and said:
"I thought it was a great game. Unfortunately we couldn't see it out, but I thought my players deserved some credit.
"We saw two teams wanting to win a football match and that'll always make an entertaining game.
"You've got to give credit to Bristol City. They're on a fantastic run and they've got a bright young manager. It's a club going in the right direction and they reason they score goals is because they've got good players.
"I think that when you go away from home you play without fear. I'm very proud of my players this week like I always am."
