News of Wilder's new deal broke before United's clash with West Ham at Bramall Lane last night, and the Blades celebrated in perfect fashion with a 1-0 victory to move up to fifth in the top-flight table.
McBurnie scored the winner after unselfish work from John Fleck, while VAR worked in United's favour for a chance by ruling out a stoppage time goal from Hammers' Robert Snodgrass after spotting a handball in the build-up.
United also have the option in their favour to extend Wilder's contract by a further year and McBurnie, his record signing, said: "The gaffer and staff have created something special and a lot of players have as well, so to see him and the staff rewarded and commit their futures is great for the boys and the club."
Asked what it was like to play for Wilder, McBurnie admitted: "Not easy!
"It can be tough at times but that's sometimes what I need.
"He knows how to get the best out of players - he's great at man-management and got the motivational side of it too.
"He can get more out of players than other managers can, so it's great to work with him and learn from him.
"The boys are coming on leaps and bounds and I think you can see that in our performances."