Billy Clarke's fourth goal of the season midway through the first period proved enough to register all three points for McCall's men - their third victory on the road so far this campaign.
Coming on the back of Tuesday's success at home to Fleetwood Town, the Chesterfield win made it six points in a week for City, moving them up to second in the Sky Bet League One table.
After a dominant display from the players in claret and amber, McCall was understandably happy by the Bantams' latest efforts; his only minor criticism was that the victory wasn't by a greater scoreline.
McCall said: "It was a good performance from us, a really good performance, and a great result.
"It would have been nice if we could have made things a bit more comfortable at the end. In the first half in particular, we've played some terrific stuff.
"We've created some good chances. In fairness to our lads though, it wasn't really missed chances, it was more a case of good goalkeeping.
"The second half was a bit more even but we still looked like we could score more. We've also managed the game really well - another clean sheet.
"Doyley (Colin Doyle) has only really had one meaningful save to make but that was an outstanding one from their free-kick in the first half.
"Chesterfield have scored a lot of goals at home so far this season so we knew there would be moments when we had to stand up and be counted - you can't dominate a game completely for ninety minutes.
"The only slight disappointment from today (Saturday) is that we haven't won by more. We've still got the three points though, and that is all that ultimately matters."
Billy Clarke's winning goal came after he was found in space in the box via some quick thinking from Nicky Law at a corner.
McCall said: "We actually changed things up slightly yesterday (Friday).
"We put Jordy (Hiwula) on the goalie rather than Clarkey and we just asked Billy to be alive to get on it in the box if it was on.
"You would still expect him to get picked up but I think because we had six in the box for that particular corner rather than five, maybe that threw them a bit.
"From our point of view, it is good, bright thinking by Lawsy (Nicky Law), a good turn by Clarkey and then a terrific finish."