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 Championship game at The City Ground 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.
Leeds' dominant on-field display was almost a backdrop to a celebration of Speed's life off it, though.
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 and it was during that vocal tribute that they opened the scoring.
They had started the better of the sides with Snodgrass twice going close, before Becchio's flick played in Howson and he drew a save from Lee Camp. Michael Brown, making a first start since September 10, then worked the keeper somewhat harder from 30 yards.
The pressure soon told and in the 20th minute, Leeds took the lead. Snodgrass picked up possession midway through the Forest half and, after a handful of paces, he beat Camp with a crisp left-footed drive from 20 yards. The goal was celebrated no more vehemently than by Grayson who was close to breaking down on the sidelines.
Forest had no answer to Leeds' pressure and Becchio soon broke through looking to make it two but Joel Lynch made a last-ditch saving tackle, before Lynch's defensive partner Wes Morgan made an even more impressive block.
Seven minutes before the break Snodgrass got clear and, although Camp left his goal to meet him, Snodgrass won the tackle between the two. He then tried to find the vacant goal but Morgan managed to get back and deflect his 25-yard effort over.
A jinking run from Snodgrass then laid on a simple chance that Howson should have finished, although it mattered little as the two combined to greater effect just seconds later.
Becchio's touch found Snodgrass, whose cushioned pass set Howson free down the right. He was still 25 yards from goal but hit a first-time half-volley that gave Camp no chance and found the top corner for his first goal since his effort during a 4-1 win over Forest in April.
Forest introduced the powerful Ishmael Miller at half-time in a bid to start a rescue mission, but their task got all the harder in the 49th minute when Becchio rose to head in a Brown cross for his second of the season.
Miller's arrival did give his side a new outlet, though, and his header, although comfortably held by Alex McCarthy just before the hour, marked his side's first real chance.
However it was only a momentary spark for Forest and with 24 minutes left Leeds made it four. Howson robbed Greg Cunningham of possession just outside the area and, although his shot was parried by Camp, Clayton was on hand to despatch the rebound.
Forest midfielder Andy Reid saw red for a second yellow card with 11 minutes to go to cap an awful night for his side.