Jonathan Woodgate's Boro had offered little attacking threat, as they went in search of their first away win of the season in the Championship.
Forest have only scored 10 times at home this season – and that lack of ruthlessness cost them again.
The Reds dominated the opening exchanges but, despite a flurry of threatening moments, it took until the 15th minute for Joe Lolley to muster the first effort on goal, with a curling shot that Aynsley Pears was well placed to save.
A darting, powerful break down the right from full-back Matty Cash carved out another opportunity, but his shot was wayward.
Grabban flashed a header inches wide – but was ruled offside either way.
Ashley Fletcher sent a header too close to keeper Brice Samba, as Boro threatened for the first time. Lolley was unselfish when he squared to Grabban instead of shooting – but the striker could not quite connect, at full stretch. Forest had dominated the first period, but could not make it count.
Forest had scored only seven of their 26 goals prior to this fixture in the first half of games – and the pattern was continued, against a Middlesbrough side who had a seven-man rearguard at times.
Ben Watson's header sent the ball back into the danger zone from an early second half corner, but again Forest could not profit. Ameobi did his best to conjure something on his own, but a brilliant turn and shot ended with another smart save from Pears.
Yates then hit the bar with a driven volley as Forest continued to push.
And Middlesbrough's resolve was finally broken in the 63rd minute, when Cash delivered an enticing cross to pick out the timely run of Yates, who this time sent the ball into the back of the net with a powerful header.
Grabban did brilliantly to hold off two Boro defenders with great strength, but then chose to pass to Watson, rather than shoot from a good position – the chance went.
Forest should have had the game wrapped up – but instead handed their visitors a lifeline, when Robinson clipped the heels of sub Johnson in the penalty area.
McNair emphatically converted from the penalty spot, to draw Middlesbrough level and earn a point that had seemed unlikely for long spells.