Billy Clarke fired home his fourth goal of the campaign and his second in as many games to earn the Bantams a deserved win.
McCall would have liked the scoreline to reflect their dominance, but overall he could not complain.
“First half, we played some terrific stuff, created a lot of opportunities and it was good goalkeeping from them to stay in it,” said McCall.
“At the end of the day, that’s what we’re after, a win, but it would have been nice if it was a bit more comfortable.
“It was another clean sheet after Doyley (Colin Doyle) made one outstanding save. All through the side there’s been some big, big performances and, most importantly, we’ve got three points.”
The Bantams dominated from the start in front of almost 2,000 travelling supporters and struck in the 26th minute. Clarke picked up a short corner and slammed his effort into the roof of the net from the edge of the area.
The visitors could have put the game to bed before the break as the Spireites rarely threatened.
Jordy Hiwula-Mayifuila and Mark Marshall both fired off target before the latter forced Ryan Fulton into a top stop.
The hosts’ only chance came when Doyle tipped over Kristian Dennis’s thunderous free-kick.
After the break, Fulton kept the arrears to one with a reaction save to keep out Hiwula-Mayifuila’s flick.
Chesterfield: Fulton, Graham, Maguire, Hird, Anderson, Ariyibi, Mitchell (O’Shea 46) Liddle, Nolan (German 76), Wilkinson, Dennis (Dimaio 63). Unused substitutes: Parkin, Evatt, Gardner, Humphreys.
Bradford City: Doyle, Darby, Vincelot, Knight-Percival, Meredith, Marshall, Cullen, Dieng, Law (Morais 78), Hiwula, Clarke (Vuckic 78). Unused substitutes: Sattlemaier, Rabiega, McArdle, Devine, Kilgallon.
Referee: D Bond (Lancashire).
Man of the match: Mark Marshall.