A victory for the league's bottom side would have taken them above Wigan Athletic, who do not play until Tuesday's trip to Reading.
And, on a difficult surface, Lee Clark's men made a solid start as Gary Madine's goal gave them a lead at the break before Andrea Orlandi doubled the advantage after the hour.
However, with 20 minutes remaining, Forest were level after goals from Dexter Blackstock and Gary Gardner, with goals apiece from Blackpool's Steve Davies andForest's Henri Lansbury then coming either side of Tom Aldred's dismissal.
The late drama continued as Chris Burke and David Ferguson each scored in stoppage time with Dougie Freedman's unbeaten start at Forest maintained.
On any other weekend, Watford's 4-3 victory over Bolton Wanderers would have been the standout game with no shortage of drama at the Macron Stadium as Troy Deeney's late winner settled things after Bolton had come from 1-0 down to lead 2-1.
At the summit, Bournemouth moved back top on goal difference but could have made more of Middlesbrough and Derby County's league absences had they not been held 1-1 by Huddersfield Town.
With Derby and Boro both in FA Cup action, Yann Kermogant's opener looked set to send Bournemouth two points clear before Eddie Howe's men were denied by James Vaughan's second-half leveller.
Daryl Murphy's first-half brace was enough for Ipswich Town in their 2-1 win at Fulham as Mick McCarthy's side bolstered their play-off hopes, while Charlton Athletic put three past Brentford without reply.
Johann Gudmundsson, Igor Vetokele and Frederic Bulot were the men on target against their near neighbours while Norwich City made it three wins on the spin against Wolves courtesy of goals from Bradley Johnson and Lewis Grabban.
Alex Mowatt's first-half winner proved the difference for Leeds United against Millwall at Elland Road while Sheffield Wednesday's visit of Brighton and Hove Albion ended goalless.
