A catastrophic error from goalkeeper Ryan Clarke sent Oxford United tumbling to a shock first home defeat of the season - as they missed out on the chance to return to the top of the table.
There didn't look to be too much danger when Iyseden Christie sent in a speculative 20-yard shot in the 28th minute, with Clarke saving above his head.
But the ball squirmed out and dropped over the line, just inside his left post.
United never really fired going forward, on an energy-sapping pitch, and to complete their miserable afternoon, they had substitute Damian Batt sent off in stoppage time for dissent.
Wilder gave debuts to Jake Wright and Anthony Tonkin, but there was no place, even on the bench, for the third new signing, Lee Fowler.
Up front he went for a three-man attack of Alfie Potter, James Constable and Franny Green.
There was nothing wrong with the start Oxford made, and they had three shots in the opening four minutes, two of them forcing saves from keeper Dan Alcock.
Potter elected to shoot early with his nopportunity and hit it past the far post, Constable cleverly let the ball run from Mark Creighton's ball over the top, and had a low shot saved, and then, from a flowing move, Potter fed Constable to his right and the centre forward rifled in a drive that the keeper again got behind.
With two changes in the back four, and Adam Chapman somewhat vulnerable at right back, United did not look comfortable in defence, although Tonkin soon began to show what a classy player he is.
It took an excellent last-ditch challenge by Creighton to stop one raid, and the visitors began to make serious inroads down Oxford's right.
Tamworth almost took the lead on 25 minutes when Tom Shaw was left totally unmarked at a corner, and he sent a volleyed shot against the bar from the edge of the area.
But three minutes later, disaster struck for the U's as Clarke allowed Christie's shot to drop from his grasp, and roll over the line.
There didn't seem to be much sharpness in Oxford's team, a result no doubt of not playing for three weeks.
After fine play from Franny Green, who squared it on a plate, Potter wanted too much time in front of goal, and his over-deliberate side-footed shot was saved.
Tamworth were looking just as likely to add a second goal as the home side were of equalising, and Michael Briscoe tried his luck with a long-range effort that wasn't far away.
In the second half, Wilder threw on Damian Batt, Matt Green and Jack Midson to try get United back at least on level terms, but Tamworth defended for their lives.
Indeed, Bradley Pritchard had an opportunity to double their lead, but hesitated and was dispossessed.
Hesitation was proving costly everywhere, and when Constable saw a shot blocked and the ball ran to Matt Green, he opted to take a touch rather than shoot first-time, and his shot was then charged down.
Constable, the only United player who looked like scoring, had a header saved at a corner.
There were six minutes of stoppage time after some blatant timewasting from the Lambs, but United just couldn't find a way through.
Right at the death, Matt Green almost saved a point, but his shot from ten yards was saved by the keeper's foot.
Oxford Utd: Clarke, Chapman (Batt 53), Creighton, Wright, Tonkin, Bulman, Murray, Clist, Potter (Midson 64), Constable, F Green (M Green 53). Subs not used: Turley, Day.
Referee: John Hopkins (Essex) Att: 5,690 (141 from Tamworth).
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