There was a minute’s silence for the 25-year-old before Thursday’s Super League clash at Halliwell Jones Stadium.
Stevenson, originally from Harrogate, suffered a head injury playing for the RAF against the Army last Friday and tragically died on Monday.
Knaresborough-born Minikin, 24, told The Yorkshire Post: “Scott’s my brother Lewis’s best pal so we grew up together.
“They started playing rugby together (at Harrogate RUFC) when they were six so I’ve known him from when I was five years old.
“It was terrible when I heard, He was a great kid, an absolute legend. Anyone you speak to will tell you that. I just want to get across how much of a nice guy he was.
“I’ve seen loads of stuff on social media about how good of a kid he was and it’s so true.
“I just feel for the family. We’re really close family friends. Everyone is heartbroken.
“The minute’s silence tonight was emotional – and we got the win for Scott.”
Tigers winger James Clare put an arm around his team-mate after the tribute at the televised tie as they prepared for kick-off.
Minikin conceded: “I was a bit worried how the minute’s silence would go and then going straight into the game.
“But you just have to get on with it. It was really emotional. I’m just glad we won and it was a great effort from the boys.”
Earlier in his career, Minikin played alongside Stevenson for York City Knights Under-18s.
The club will also hold a minute’s silence when they host Featherstone Rovers in today’s Championship play-off.
Meanwhile, Castleford head coach Daryl Powell hailed his depleted side as they defied the odds to eliminate Challenge Cup holders Warrington with a gritty 14-12 win.
He said: “It was a huge effort from everybody. We asked our senior players for their season’s best performances and they pretty much delivered it. If you look at the amount of high quality players we had watching the game, it was always going to be tough.
“Buut we believed we could win. Not many others did but defensively I thought we were superb. We showed resilience and held our nerve consistently across the game.”
Tigers will travel to Salford Red Devils in a final eliminator on Thursday evening.
Ian Watson’ side went down 18-12 at Wigan Warriors last night, with the hosts set to play St Helens for a place in the Grand Final on Friday night.
Another tight play-off game saw the sides tied 6-6 at the break.
Oliver Gildart, Thomas Leuluai and George Williams scored Wigan’s tries with Zak Hardaker booting three goals. Salford’s tries came from George Griffin and Jackson Hastings, with Kris Inu adding the conversions.