Grayson signed schoolboy forms with Leeds on the same day as Speed when the pair were 14, and he also played, trained, roomed and earned his coaching badges with the former Toon star.
Off the field, fans paid their tributes to Speed with a minute's applause.
But the traveling support also stuck to a pre-match plan of singing Speed's name for 11 minutes - 11 being his old shirt number - during the first half. At full-time, Grayson went to the away end and pointed to the sky before leaving the field in tears.
Simon Grayson: "It's been a difficult couple of days for myself and Gary's family, supporters of Leeds United and supporters in general.
"Gary Speed was a fantastic person and I wanted my players to go out and produce a performance for him tonight.
"That was right out of the top locker of our performances tonight. It was very poignant that the first goal came right as the 11 minutes of singing ended and was a left-footed shot.
"Gary Speed scored many goals like that. It's been difficult, but I'm a very proud manager tonight. I'm delighted to have got a result for Gary Speed.
"It has been a very difficult time. I had to put my professional head on, but during the minute's applause it was difficult to keep concentration.
"But I had to do it, because I knew he would want us to put on a performance and the manner or how we played was a reflection of what Gary would have been delighted with."