However, Billy Davies' men were made to pay for not taking full advantage of their early dominance as Leeds levelled through Lloyd Sam and it was the visitors who appeared more likely to grab a winner during a scrappy second half.
The result means both sides are still looking for their first league victory of the season, although United will take plenty of encouragement from a spirited display.
Forest boss Davies made seven changes to the side beaten by League Two Bradford
in the Carling Cup, with Kelvin Wilson, Paul McKenna, Robert Earnshaw and Blackstock among those to return.
Richard Naylor replaced Alex Bruce in the heart of the Leeds defence as Simon Grayson reverted to the XI that lost 2-1 to Derby on the opening day of the season.
The hosts may have been expected to be low on confidence following a shaky start to the season, but they showed no sign of nerves as they dominated the early exchanges.
Paul Anderson had already forced Kasper Schmeichel into a sharp save by the time Forest opened the scoring.
Chris Gunter's first-time cross from the right picked out the unmarked Blackstock and the striker guided a header beyond Schmeichel and into the bottom left corner.
Forest almost added a second five minutes later following some delightful interplay between Blackstock and Earnshaw, but the latter's shot cannoned off the post.
Leeds were on the rack at this stage, but they eventually weathered the storm and created a chance of their own in the 24th minute when Luciano Becchio was denied by the onrushing Lee Camp.
The visitors continued to improve as the half wore on and drew level nine minutes before the break through Sam's first league goal for the club.
Wes Morgan needlessly gave away possession in his own half and the resulting attack ended with Bradley Johnson delivering a superb cross from the left for Sam to head home.
Forest attempted to lift the tempo after the interval, but struggled to reproduce the free-flowing football that put Leeds under such pressure early on.
Indeed, it was the visitors who started to look increasingly assured in possession and they almost went ahead when Sam's dangerous low cross flew across the face of goal.
United came close again in the 70th minute as Sanchez Watt headed narrowly wide
from a corner.
Forest goalkeeper Camp then suffered a cut above his left eye following an accidental collision with Naylor, although he was able to continue following treatment.
Tempers flared in the 79th minute after Gunter petulantly stamped on the foot of Watt during a break in play. Both men were booked by referee Tony Bates, although the Forest full-back can consider himself fortunate not to have seen red.
Leeds continued to enjoy the better of proceedings as the final whistle approached, but they were unable to find a winner.
Nottingham Forest: Camp, Gunter, Morgan, Wilson, Bertrand, Cohen, McKenna, Majewski, Anderson, Blackstock, Earnshaw.
Subs: Darlow, Chambers, Adebola, Tyson, McCleary, Moussi, Thornhill.
Leeds: Schmeichel, Connolly, Collins, Naylor, Kilkenny, Becchio, Sam, Howson, Johnson, Watt, Bessone.
Subs: Bruce, Higgs, Grella, Clayton, Hughes, Bromby, White.