Isaiah Jones’s first-half winner proved sufficient to secure the first home win in Wilder’s Riverside reign, with Boro recording just two efforts on target.
Swansea had much better chances, but thanks to a combination of some excellent Middlesbrough defending, some poor Swans finishing and a couple of contentious decisions from referee Andy Davies, the hosts held on to claim a victory that lifts the Teessiders to within four points of the play-off positions.
Wilder said: “We showed different qualities and found a way to keep the ball out of the back of the net.
“Was that the way we want to play? Was that as we’ve played the last three? No.
“We turned the ball over cheaply and I think we’re better than that.
“That was the nature of the game, but what we did show was the quality to get the blocks in and clear one off the line.
“We’ve talked about playing well and if you can’t play well then you have to come out and find a way to win the game.
“We didn’t play as well as I would have liked but we got a win and it just shows you what a crackers division it is off the back of the Millwall and Preston games.”
Jones’s goal was his first in a Boro shirt and Wilder was happy with the composed manner in which the 22-year-old slotted a low finish past Ben Hamer.
Middlesbrough: Daniels, Anfernee Dijksteel (Fry 90), Bamba, McNair; Jones, Crooks, Howson, Tavernier, Bola, Sporar (Ikpeazu 73); Watmore (Hernandez 72). Unused substitutes: Lumley, Taylor, Payero, Lea Siliki.
Swansea City: Hamer, Cabango, Naughton, Rhys Williams (Obafemi 67); Laird (Latibeaudiere 78), Grimes, Downes, Manning; Smith (Ntcham 46), Paterson, Piroe. Unused substitutes: Benda, Bennett, Cullen, Bidwell.
Referee: A Davies (Hampshire).