Derby manager Steve McClaren looked on course to collect his third win since taking charge when Jamie Ward scored his third goal in a week to give Derby a deserved first-half lead.
But Birmingham showed character after the break and drew level when substitute Novak volleyed past Lee Grant in the 66th minute to halt a run of five away defeats in the Sky Bet Championship.
McClaren made changes at the back with on-loan Liverpool defender Andre Wisdom coming in for his debut at right-back, while Jake Buxton replaced injured centre-half Zak Whitbread.
And it was Buxton who put Ward through in the second minute only for Darren Randolph to turn his shot behind for a corner.
Birmingham responded by forcing a corner, which Nikola Zigic headed over from eight yards out, but Derby always looked the more dangerous team.
They went close again in the 29th minute when Craig Bryson lifted the ball over Randolph only for Dan Burn to clear off the line.
The movement of Derby's midfield was causing problems for the visitors but Zigic almost put them in front when he headed Shane Ferguson's corner against the bar.
Birmingham lost influential winger Chris Burke to injury in the 36th minute and they went behind three minutes later when Bryson's low cross from the left found Chris Martin, whose near-post flick was saved by Randolph only for Ward to turn the loose ball in.
Derby's only moments of concern had come from set plays and Birmingham threatened again at the start of the second half when Zigic headed a corner narrowly wide.
The Rams remained in control and both Ward and Will Hughes almost got through the visitors' back line before Birmingham stunned the home fans with an equaliser in the 66th minute.
Novak had only just come on when a long diagonal ball over the top from Paul Caddis found him unmarked at the back post and, as Derby looked in vain for an offside flag, he smashed a volley into the top left corner of Grant's net.
Derby almost regained the lead when Hughes put substitute Mason Bennett in on the right, but his low shot was scrambled clear at the near post.
Birmingham escaped again in the 81st minute when Burn misjudged the bounce and Conor Sammon flashed a shot just wide from 15 yards.
There was one final chance for Derby in stoppage time when a free-kick was hooked back in after it had bounced clear off the wall, but Sammon could not keep his header down and the visitors were able to celebrate collecting a vital point.