After a dull first half on Wednesday night, the game livened up and Well goalkeeper Darren Randolph made a fine save from Rui Miguel before Steven Hammell beat Cameron Bell with a free-kick from 25 yards only to see the ball hit the crossbar on its way over.
However, in the 81st minute Killie defender Tim Clancy sent in a great cross from the right which allowed Silva, on for Willy Aubameyang with less than 20 minutes remaining, to score the winner from close range.
In a dramatic finale, Kilmarnock skipper Garry Hay picked up a straight red card for a foul on Chris Humphrey but the visitors held out.
The visitors had lost their top two goalscorers going into the game with Conor Sammon having signed for Wigan on transfer deadline day and midfielder Jamie Hamill suspended.
Midfielder Alexei Eremenko returned from a ban while French striker Aubameyang replaced Sammon to make his first start.
Well manager Stuart McCall took the opportunity to freshen up his side as Steve Jones and Esteban Casagolda came in for Tom Hateley and John Sutton, who both started on the bench.
The lashing rain and driving wind which arrived in time for kick-off did little to help the spectacle but in the fourth minute Jamie Murphy raced onto Keith Lasley's long ball and flicked it over the advancing Bell, only for Mohamadou Sissoko to get back to clear.
Moments later Humphrey had an angled drive from just inside the box after getting past Hay, but Bell was in the right place to gather.
Kilmarnock came back into the game with the talented Eremenko pulling the strings in midfield, although a cheeky attempt at a lob in the 19th minute from 40 yards failed to find the target as Randolph raced back after making a clearance.
Liam Kelly was booked in the 32nd minute for a foul on Lasley as referee Stevie O'Reilly tried to put an end to the infringements which had begun to mount up.
The home side won the first corner of the game three minutes later but it was easily defended by the visitors.
Five minutes before the break Killie defender Frazer Wright was carried off on a stretcher after a clash with Motherwell defender Steven Saunders, to be replaced by James Fowler.
Motherwell started the second half better and in the 50th minute midfielder Steve Jennings slipped in Murphy but under pressure from Fowler, his effort from 14 yards lacked the power to trouble Bell.
At the other end Clancy found himself racing into the box with time and space but dragged his shot wide of the far post.
The Steelmen stepped up the pace and in the 56th minute Humphrey's low corner from the left almost sneaked past Bell.
But in the 61st minute it was Killie came closest to opening the scoring when Rui Miguel got on the end of a Hay cross but his flick was saved down at the near post by Randolph.
The Steelmen stormed back and Bell made a good point-blank save from Murphy after he
had worked his way past Sissoko.
As the game appeared to be swinging towards the home side, Well defender Steven Hammell beat Bell with a free-kick from 25 yards but it struck the top of the crossbar before going over.
Bell made another good block from Jennings but in the 81st minute Silva raced into the box to get on the end of a Clancy cross to head in the winner.
However, before the final whistle Hay picked up a straight red card for a blatant foul on Humphrey as Motherwell broke.