A minute's applause was held and players from both teams wore black armbands in tribute to Speed, who started his career at Elland Road and won the first division title with the club in 1992.
And Grayson's men heeded their manager's call to put in a special performance, with goals from Robert Snodgrass, Jonathan Howson, Luciano Becchio and Adam Clayton before Forest's Andy Reid was sent off late on.
Leaders Southampton were forced to come from behind to equal their post-War record of 21 straight home victories in all competitions as they nudged past Hull City 2-1. Robert Koren put the visitors ahead in the 43rd minute but Saints hit back through Guly Do Prado before Adam Lallana headed the winner. Hull substitute Robbie Brady was sent off 11 minutes from time.
Second-placed West Ham stayed within two points of the Saints after securing their seventh away win of the season at Middlesbrough. Frederic Piquionne opened the scoring with a ninth-minute header and Carlton Cole made it 2-0 in injury time.
Leicester promised better times ahead under Nigel Pearson at the King Power Stadium with a 2-0 win over Blackpool. Andy King scored a 35th minute opener and Neil Danns added the second eight minutes from time.
Craig Mackail-Smith scored the only goal of the game as Brighton edged Derby 1-0 at Pride Park, while Chris McCann's double helped Burnley hammer struggling Ipswich 4-0, with further goals from Sam Vokes and Jay Rodriguez.
Bottom club Doncaster went down 3-2 at Millwall, for whom Liam Trotter's two first-half strikes sandwiched a Billy Sharp penalty. Darius Henderson extended Millwall's lead before Sharp's second four minutes from time.
Bristol City maintained their good run as they came from 2-0 down to draw 2-2 at Watford. Carl Dickinson and Craig Beattie put the home side in front but Marvin Elliott and an Adrian Mariappa own goal gave the visitors a point.
Late goals from Adam Le Fondre and Hal Robson-Kanu helped Reading to a 3-2 win over Peterborough at the Madejski Stadium. Tommy Rowe put Posh ahead before Simon Church equalised for Reading. Emile Sinclair scored a last minute consolation for the visitors.