Gary Rowett's side headed into the match unbeaten in eight, and it was they who called the shots in the first period.
In the 37th minute, Johnny Russell unleashed a vicious free kick and rattled the visitors' crossbar, and that was as close as either side came before the half-time whistle.
The Robins were forced to replace Fielding with Luke Steele at the interval as their first-choice goalkeeper had taken a knock, but his replacement proved up to the task of shutting Derby out for the remainder.
The Rams surged forward again in the 64th minute with Russell leading the charge, the striker's cross finding Tom Lawrence inside the box, but Steele was on hand to tip the midfielder's shot over the bar.
Steele was called into action again minutes later when David Nugent's through-ball was collected by the in-form Vydra, but the Bristol keeper made himself big to thwart the striker at close range and maintain the parity.
There was controversy in the 87th minute when Flint caught recent Rams signing Cameron Jerome in the penalty area, only for the referee to book the Derby striker for alleged simulation.
After spending much of the game under the cosh, the Robins almost snatched three points against the run of play when Korey Smith shot from the edge of the D, but his effort bobbled inches wide.
The draw halts a run of five successive defeats in all competitions for Bristol, while Derby remain in the automatic promotion places with a two-point lead over Cardiff City in third.
DERBY COUNTY (4-2-3-1): Carson; Wisdom, Keogh, Davies, Forsyth; Thorne, Huddlestone; Russell, Vydra (Jerome '76), Lawrence (Weimann '76); Nugent (Winnallat '76)
BRISTOL CITY (4-4-1-1): Fielding (Steele '45); Wright, Flint, Baker (Diedhiouat '45), Magnusson; Brownhill, Smith, Pack, Bryan; Paterson; Reid