Wales manager Speed was found dead at his home on Sunday aged 42 and Leeds, with whom he won the old First Division title in 1992, were the first of his five former clubs to play since the tragic news broke.
Manager Simon Grayson, who forged a lifelong friendship with Speed after they signed schoolboy forms with Leeds on the same day when they were 14, asked his players to win the game in Speed's memory.
And they duly produced their best performance of the season to do so, with first-half goals from Robert Snodgrass and Jonny Howson and second-half strikes from Luciano Becchio and Adam Clayton doing the damage.
Prior to kick-off the two sets of fans shelved historic animosities dating back to the feuds of Brian Clough and Don Revie to join together in a minute's applause, while the travelling support chanted Speed's name for 11 minutes during the first half. Speed predominantly wore that shirt number throughout his 312 appearances for Leeds.
Forest midfielder Andy Reid saw red for a second yellow card with 11 minutes to go to cap an awful night for his side.