In a hugely entertaining clash, Knight had given the Blues an early lead before the visitors levelled before the break.
However, a fine individual strike by Doyle then restored our lead early in the second half before Knight struck again.
And though the Baggies threatened a late comeback by narrowing the deficit, Nmecha then put the seal on a fine City performance to put the young Blues through to a fourth FA Youth Cup final in five years.
Prior to kick-off there was a minute’s applause which was held in honour of former Club Secretary and our Life President Bernard Halford, who sadly passed away last week, with the City players also wearing black armbands.
Once the action got underway the Blues immediately got on the front-foot seeking to take the game to the visitors as they probed and tested the Baggies back-line.
And on 10 minutes City's early dominance was rewarded with a fine opening goal.
Full-back Jeremie Frimpong was the inspiration driving forward 30 yards before finding Adrian Bernabe on the left flank.
The Spanish winger cut inside before fizzing in a low cross which was superbly converted home from 10 yards out by Ben Knight, the youngster’s exquisitely-crafted shot curling inside the right-hand corner of the net.
Not surprisingly the early strike only boosted the Blues’ confidence and Bernabe almost doubled our lead on 18 minutes after a fine pass from Nabil Touazi put him clear, however Albion keeper Josh Griffiths kept out a stinging low drive with his feet.
But the Blues’ crisp passing and clever movement combined to create another opening on the half hour as Ben Knight’s delicate inside ball saw Doyle drill in a powerful effort which Griffiths parried away.
Out of nowhere however the Baggies drew level on 33 minutes after robbing City of possession midway in our half.
Jamie Soule drove into the edge of the box before twisting and opening up space and then unleashing a fine curling shot which beat a diving Moulden and went inside the right-hand post.
City almost summoned up an immediate response as Ben Knight’s rasping 20-yard shot arrowed just wide as the balance of play switched one way then another.
Four minutes from half-time City’s hearts were in their mouths as Albion almost took the lead after Taylor Harwood-Bellis slipped bringing the ball out of defence.
Morgan Rogers went in for the kill, firing in a seemingly goal-bound shot but Harwood-Bellis then redeemed himself by racing back before producing a brilliant goal-saving block a yard from the goal-line.
In what was now an absorbing contest, Felix Nmecha came within an ace of restoring the lead for City, his 25-yard drive missing the target by mere inches as the first half ended with honours even.
Just as in the opening period, City began the second half the brighter with Bernabe and Harwood-Bellis both threatening before Rowan McDonald’s 25-yard effort sailed just over.
And on 53 minutes City got our reward through Tommy Doyle. The midfielder let fly from 25 yards and the Albion keeper slipped at the crucial moment with the ball nestling in the back of the net to restore our lead.
Gareth Taylor’s side then came within an ace of making it three on the hour when, after Bernabe had once more caused havoc on the left flank, Nmecha thundered in a stunning effort which cannoned back off the crossbar.
The Blues kept on the front foot with Bernabe then seeing a brilliant low drive whistle just wide.
But the third goal City so deserved did finally arrive on 78 minutes with Ben Knight bagging his second of the evening.
Doyle was the provider dispatching a wicked in-swinging corner and Knight timed his jump to perfection as he guided the ball home.
The Baggies were given hope five minutes from time after a mix-up in the Blues back-line presented Rayhaan Tulloch with an open goal from six yards out and the Albion man made no mistake.
But the Blues sealed the deal a minute later when Nmecha demonstrated his skill and vision by dispatching a fine half volley to the delight of a raucous home crowd and seal a second final appearance this season following our Under-18 Premier League Cup triumph last month.
What it means
City can now look forward to an FA Youth Cup final against Liverpool with the Blues enjoying home advantage.The date and kick-off are yet to be confirmed.
How we lined up
Louie Moulden was in goal, shielded by a back four of Alpha Dionkou, central defensive duo skipper Eric Garcia and Taylor Harwood-Bellis along with Jeremie Frimpong. Deployed in midfield were Rowan McDonald and Tommy Doyle with Ben Knight and Adrian Bernabe providing the width on either flank.
Up-front meanwhile were Felix Nmecha and Nabil Touaizi.
Gareth Taylor’s side are back in Under 18 Premier League action on Saturday when we travel to Stoke City. Kick-off at the Clayton Wood Training Centre is 11am.