Windass' tenth of the season was just reward for a determined Bradford display and they could have avoided a nervous finish had a late header from skipper David Wetherall not rattled the Chesterfield bar.
Having failed to find the net in their last two home games, City started with more urgency but leading marksman Windass saw an early opportunity snatched from under his nose.
After just six minutes the veteran striker beat the offside trap on the edge of the Chesterfield box, but as he lined up his shot centre-half Aaron Downes made a vital block to snuff out the danger.
On loan midfielder Mark Hughes got the nod in place of suspended Chesterfield skipper Mark Allott and his dangerous-looking run into the City box was only halted by a timely tackle from Marc Bridge-Wilkinson.
Midfielder Bridge-Wilkinson looked the most composed as both sides struggled to create clear-cut openings and his superb pass on the half hour deserved a more clinical finish from speedy winger Jermaine Johnson.
Despite the hard-running of Paul Shaw and Colin Larkin, the visitors failed to test City keeper Donovan Ricketts in the opening period and it took another desperate block from Barry Roche and Downes to deny Tommy Black a goal four minutes before the break.
Black, who was struggling to make an impact, suddenly latched on to a pass from Eddie Johnson but again the chance went begging as Roche and Downes threw themselves at his feet.
It was the last contribution from the Bradford pair as they were both substituted and whatever manager Colin Todd said at the break had the desired effect.
Windass had a 51st minute penalty appeal waved away, but City had started the second half at a much higher tempo and it was no surprise that tricky winger Johnson played a part in his side's opener.
Referee Lee Mason initially waved play on when City man was tugged back, but after his run came to nothing the official called play back and awarded the free-kick.
Bridge-Wilkinson whipped over a teasing cross from the right after 57 minutes and Windass showed a real striker's instinct to force his way through the crowd to head home from six yards.
With the goal drought over City should have run out easy winners but a combination of poor finishing and bad luck meant the home fans' nerves were on edge until the final whistle.