Taylor poked home from close range in the 64th minute to cancel out Martyn Waghorn's brilliant first-half opener.
The Rams had enjoyed the better of the first-half chances and deservedly went ahead when Waghorn scored with a 25-yard free-kick on the half-hour mark.
And Taylor made him pay for the miss when he equalised following a goalmouth scramble from a 64th-minute corner.
Derby thought they had won it late on when Kamil Jozwiak had a goal ruled out for offside.
The point lifts Derby out of the early relegation zone and leaves Forest still looking for a first home win of the campaign.
Sammy Ameobi fired a long-range effort straight at Marshall in the 16th minute.
Curtis Davies failed to find the target with a header in the 23rd minute after Lawrence's cross had too much pace on it.
Yates weakly headed wide from Ameobi's cross minutes later when he had time to pick his spot.
Samba saved a powerful Shinnie's shot from the edge of the box in the 27th minute.
Waghorn put the Rams ahead with a superb 25-yard free-kick that went in off the crossbar on the half hour.
Shinnie should have doubled the lead when he shot straight at the keeper after Nathan Bryne played him in seven minutes later.
Yates headed straight at Marshall from Nicolas Ioannou's cross on the stroke of half-time as Forest continued to struggle for ideas.
Ameobi had two shots charged down just after the restart as Forest looked to create pressure.
Lawrence had a long range shot deflected behind, before Waghorn headed wide from the resulting corner in the 54th minute.
Marshall turned an Anthony Knockaert cross behind as Ameobi prepared to pounce, but Forest levelled from the resulting corner when Taylor slotted home from inside the six-yard box.
Taylor headed wide from an Ioannou cross in the 68th minute, before Taylor and Lolley were unable to get on the end of a Christie cross seconds later.
Jozwiak had a goal ruled out by the linesman after Waghorn strayed into an offside position with 13 minutes left.
Buchanan had a shot deflected behind with five minutes to go as County pushed for a late winner.