The Baggies took the lead in the 28th minute when Jayson Molumby pounced on a loose ball in the area during a difficult period for the home side when they were left annoyed by some of referee Michael Salisbury’s decisions.
But Boro recovered after Wilder introduced Duncan Watmore and Andraz Sporar from the bench in the 54th minute – and six minutes later Paddy McNair levelled.
Marcus Tavernier converted Isaiah Jones’ latest assist nine minutes later to secure maximum points for Middlesbrough, who have won seven home league games in a row in a single season for the first time since 1997-98.
Wilder said: “We are proud of our record here, we have worked hard to get these wins, they haven’t come easy, but we want to keep it going.
“It is important this place is a tough place to get a result until the end of the season.
“We are all trying to stick runs together, I haven’t got a crystal ball, the fans are seeing progression in terms of how we are playing and having a go for the football club. I really think everyone can see that, we are all in and we are enjoying it – especially nights like tonight.”
The victory lifted Middlesbrough up to sixth, after recovering from Saturday’s defeat at Bristol City.
Wilder added: “At 8.15pm it was a tough night. I was happy with how we started then after some baffling decisions from the referee we all got frustrated, including me.
“I thought there were some poor decisions, especially the Isaiah Jones one (when Conor Townsend appeared to pull him down), when I was told minimal contact by the fourth official! That was a game-changing decision.
“We had to calm everyone down at half-time and get back to what we are good at in the second half.
“The players and supporters needed a lift, we did start off better in the second half, but we mixed our game up a bit. Duncan, Andraz and Aaron – the front three – were a major problem to them.”
West Brom are wondering where the next victory will come from. The slide down the table, which started before Bruce’s appointment, has continued despite Molumby, on loan from Brighton, ending the Baggies’ run of five matches without scoring.
There was satisfaction to see the eight-hour wait for a goal come to an end but Bruce knows they need to start winning soon to close the six-point gap on the play-off zone.
Bruce, winless in four games since taking charge, said: “I’d have loved a couple of wins but it hasn’t been the case.
“We need to turn it around quickly if we are going to mount something. We have 13 games left and eight at home, I am still sure we can make a fist of it.
“The club have made me welcome, so have the supporters and I am determined to turn it around. I do believe if we can win a couple of games we can be there or thereabouts.
“I was very pleased with the first half performance, from where we were at the weekend it was night and day. Unfortunately, second half we have given two poor goals away, made mistakes and been punished.
“We just didn’t control the game like we did (in the) first half. The substitutes Chris made made a difference to them but unfortunately at the top end of the pitch, with the players we have missing, we can’t make that sort of change.
“Our home form has stacked up a bit, but we have to improve away from home and we have to get that first win under our belt.
“We have to wait now until Monday (to face Swansea) but hopefully we can get that win then.”