Goals from Mason Holgate and Richarlison saw the Toffees through at Goodison Park as Everton try to win their first trophy since 1995.
Walcott was singled out by manager Silva afterwards, for transforming what had been a shocking contest, when introduced as a half time substitute.
The England winger has enjoyed a remarkable resurrection in recent weeks, reviving a Goodison career that seemed to be over when he was disparaged by his own support, and didn’t even make the first team squad at the start of the season.
Here, he broke Watford’s defensive stranglehold on this Caraboa Cup tie, his pace and intelligence of movement the decisive factor, after 45 minutes of football that barely qualified for that term. It was his fine cross which allowed Holgate to emphatically head Everton into the quarter final.
For Silva, it was a vital contribution. “Theo played a huge part this evening again – the change we made at half time had a big impact,” he said.
“He allowed us to build our attacks quicker, and the gaps were bigger. He helped Alex Iwobi have a bigger impact, too. Theo was really important for us.
“Theo was always a really important player for me, even sometimes when he was not playing and starting the games. He deserved it. He is in a good moment, a really important player us.”
When Richarlison confirmed victory in stoppage time, it was no more than Everton deserved…or rather Watford deserved, for a hugely unambitious performance which seemed to be based solely on the idea of going to penalties.
It created a woeful first half, notable only for the commitment of the visitors to sucking all life from the contest; straight from a Harry Potter novel, but half neon.
The first shot on target arrived a minute before half time, summing up the frigid game. But when Silva hooked the disappointing Moise Kean for Walcott during the break, things warmed up.
It was Holgate’s first goal for his club which hauled it out of the deep freeze. Before then, Alex Iwobi and Lucas Digne had seen deflected shots cannon off the cross bar, and Andre Gomes a shot cleared from the line by Mariappa.
When Watford failed to clear a corner, Walcott darted onto the loose ball on the left, and crossed back in for Holgate – who is making a fair fist of grabbing a regular first team place – to ram a ferocious header home.
With Watford finally forced to break their defensive shackles, it left space for Everton to break, and Richardson ran from the half way line onto a well timed ball from Cenk Tosun to cooly finish.