Forest stretch their unbeaten run against their bitter rivals to nine games, but still sit second from bottom in the EFL Championship table while the hosts stay in 15th.
Story of the match
Forest had the first chance of the match after just three minutes as Philip Zinckernagel got forward and into space, but his shot deflected off of Derby defender Craig Forsyth and out for a corner kick.
Two minutes later, the hosts were in front. After a turnover by Forest led to a counterattack, Forsyth sent a ball over the top to Lawrence and he evaded the offside trap, took a touch into the box and beat Brice Samba at his near post.
The goal-scorer then played a neat one-two with Ravel Morrison and Samba had to get to his right to beat away the dipping, swerving shot by the Derby skipper.
Each side had a shout for a penalty as Joe Worrall came together with Louie Sibley in the Forest penalty area and at the other end a cross from Forsyth appeared to strike Worrall's arm, but the referee waved away both protests.
On 50 minutes, the Rams were on the counterattack again. The ball was worked to Lawrence in the box and after cutting inside, his right-footed effort is saved by the hand of Samba. He then gathered in Morrison's shot from 20 yards.
Kamil Jozwiak then tried his luck only to see his chance fly just wide of the near post. Sibley then found some space on the left and played in substitute Jack Stretton, whose shot from six yards nicks harmlessly off of Scott McKenna.
The Reds should have levelled on 76 minutes as Alex Mighten slinged a ball into the path of Lewis Grabban and although the ball was just behind him, a lovely back-heel flick looked to be going in until Roos got a hand to it.
Finally, in the 82nd minute, Forest equalized. Gaetan Bong's cross wasn't dealt with by the Derby defense and Johnson's first-time volley beat Roos.
Lee Buchanan then had a chance to win it for the Rams as he outmuscled his marker and met a cross from the right, but he glanced it just wide.
Worrall then blocked Buchanan's laser-like cross behind for a corner and cut out the ensuing danger and with no significant action in four minutes of stoppage time, the points were shared.
Man of the match: Joe Worrall
While Johnson's goal gave Forest their first point of the season, it was the Reds defender who came up with several key blocks and interventions with Derby pressing.