Silva's late spot-kick made for a nervy finish for the hosts but on the whole, Nuno Espirito Santo's pack were well off the pace in this 2-1 defeat.
Failing to keep up the momentum after a magnificent win against Chelsea last week, Ashley Barnes opened the scoring with a close-range header at Turf Moor.
Chris Wood then got in on the act shortly into the second half, similarly netting from a few yards out, before substitute Silva kept his cool after winning the spot-kick.
A boost for the club-record signing who can hold his head high, but it was too little too late on a deeply disappointing evening.
The positive was £35million striker Silva showing character and converting from 12 yards for his first senior goal in gold and black. Fair play to him.
The negatives, though, were vast. For 88 minutes of this clash, Wolves completely played into Burnley's hands. They made it so straightforward for them.
Nuno tried Owen Otasowie in the free role – just off the front two – and it was an experiment which did not pay off, before it was abandoned on the hour mark.
Young American Otasowie, making his first top-flight start, was not the worst Wolves player. But the approach of not having a conventional centre forward on the pitch did not work against the physical Clarets.
An annoying tendency to play free-kicks and corners short also proved easy pickings for the hosts.
Rather than getting balls into the box quickly and sharply, it allowed the defenders to get into shape and track the runners.
Wolves went with the tried-and-trusted old way of playing against Chelsea, and it worked a treat. Here, though, they appeared to overcomplicate things.
Burnley, having only scored six goals from 12 games before this one, got two and could have easily had a couple more. Such a poor Wolves outing.
Wolves made four changes to the side which started the heroic 2-1 victory over Chelsea.
Leander Dendoncker and Willy Boly both picked up knocks in that game and neither started in Lancashire, with the former left out of the squad and the latter on the nine-man bench.
Otasowie made his full top-flight bow after impressing as a substitute against the Blues while Rayan Ait-Nouri, Max Kilman and Joao Moutinho – back from suspension – also came into the XI.
Interestingly, Otasowie – a midfielder who has previously played a fair amount of games at centre-half for the under-23s – wad deployed in the false nine role.
It seemed the aim was to confuse old-school, hard-nosed defenders Ben Mee and James Tarkowski, and allow Pedro Neto and Daniel Podence more space to wreak havoc.
There was also an onus on the wing-backs to burst forward and Nelson Semedo made a decent start to the game, linking up with Neto and seeing a low cross cleared.
Otasowie, meanwhile, won a promising free-kick which was played short by Moutinho to compatriot Neto – his effort blocked.
It was an unconventional approach from Wolves, it must be said, and things began to unravel.
Burnley, on the other hand, firmly stuck to their guns as a Dwight McNeil cross found target man Wood, whose acrobatic attempt rolled a couple of yards wide.
The Clarets did look far more comfortable than Nuno's lot, who proceeded to give away possession very cheaply on several occasions. The unique style of play was not working, at all.
Sean Dyche's charges were doing what they do well – being direct – and it did not come as a huge surprise to see them take the lead.
Barnes, minutes after being released over the top by goalkeeper Nick Pope and seeing a first-time strike stopped by Rui Patricio, was the man on the mark.
A Wolves attack which broke down was punished.
Semedo was caught high up the pitch and Charlie Taylor, on the overlap, delivered it to Barnes, who was left with the fairly simple task of nodding in at the far post. Meat and drink for him, with Kilman particularly slow to react in the build up.
The home side could have been two to the good going the interval, too, with Josh Brownhill's curling free-kick narrowly evading the target.
Make no mistake, it was a dire first half and provided Nuno with plenty of food for thought.
He decided against any changes for the beginning of the second period, though – and Burnley soon doubled their advantage amid some woeful Wolves defending.
They failed to win the first, second or third ball as Mee headed it over to Barnes, whose knock-down was thundered in from point-blank range by Wood. Again, so simple for the striker.
In a desperate attempt to get things going, Nuno made a double-substitution on the hour as Adama Traore and Silva replaced Ait-Nouri and Otasowie. The system also changed to a back four – Semedo at right-back, Romain Saiss on the left.
Traore got straight into the action, as well, as he raced to the byline and neatly floated a cross over to Neto. His header ended up sailing high and wide.
The Clarets carried on threatening. Wood outdid Kilman but saw his shot smothered by Patricio, and Barnes, unmarked, had a volley blocked.
Ruben Neves then tested Pope from long range before being taken off for Vitinha.
Towards the end, Wolves did pull one back – giving a chance to the most unlikely of comebacks. Silva, after being tripped by substitute Josh Benson, calmly slotted into the bottom corner to open his top-flight account.
And while that will prove a memorable moment for the teenager, it was not enough and this was ultimately a night where Wolves just did not perform.
Burnley (4-4-2): Pope; Lowton, Tarkowski, Mee (c), Taylor; Brady (Pieters, 68), Westwood, Brownhill, McNeil (Benson, 85); Barnes (Rodriguez, 81), Wood
Subs not used: Peacock-Farrrell (gk), Norris (gk), Bardsley, Dunne, Long, Stephens
Goals: Barnes (35), Wood (51)
Wolves (3-5-2): Patricio; Saiss, Coady (c), Kilman; Semedo, Neves (Vitinha, 76), Moutinho, Otasowie (Silva, 60), Ait-Nouri (Traore, 60); Neto, Podence
Subs not used: Ruddy (gk), Boly, Marcal, Hoever, Perry, Corbeanu
Goal: Silva (pen, 89)
Referee: Lee Mason (Bolton)