A LONG trip to Norwich City is Albion's reward following a drawn-out, gruelling encounter against Port Vale.
The Baggies won 5-3 on penalties after neither side could break the deadlock during the preceding 120 minutes.
Yet Albion had chances to clinch the victory with Rickie Lambert and Salomon Rondon having the pick of the home side's chances.
Lambert had one cleared off the line and brushed the crossbar, with Rondon also planting his header onto the woodwork.
Ultimately, Albion's fate wasn't sealed until a penalty shoot-out in front of the Smethwick End.
Tony Pulis made four changes to his starting line-up, with Brown Ideye and Serge Gnabry making their first starts of the season.
The evening didn't start well for Chris Brunt who was forced off with with a lower leg injury after just 12 minutes. He was replaced by Craig Dawson, with Chester shifting over to the left.
The opening sighting of goal was to come for Brown Ideye in the 21st minute. Rickie Lambert's looping cross from the right flank found its way on the forehead of Albion's No.9, who powered his effort just wide of Jak
Alnwick's left-hand post.
It was otherwise a low-key opening-half hour at The Hawthorns, with Albion the slightly livelier side.
Gnabry was to stir the crowd late on in the first-half with a 42nd 25-yard shot which was still rising as it cleared the Vale crossbar, with Lambert seeing his deflected shot clawed away by Alnwick.
Albion were to start the second-half with initial gusto. Lambert was denied his first competitive goal in the 47th minute when he levered himself at Dawson's cross - Anthony Grant was on the line to clear the danger.
Lambert was to go close again two minutes later. His powerful blast looked destined for the top corner only for Alnwick to reach out and tip the shot over.
And, so, onto extra-time. Rondon was the first to try his luck. Lambert's lofted ball fell into Rondon's path...but he dragged the shot wide.
Rondon's luck wasn't to change. The chance of the night came in the 108th minute. A McManaman ball fell into Rondon's path but his header bounced against the bar. Seconds later McClean saw his close-range header parried by Alnwick.
Lambert was to test Alnwick once more just four minutes from time. His deflected long-range shot was brilliantly saved by the Vale keeper. Nil all it remained - the game was decided by penalties.
Rickie Lambert, Claudio Yacob scored either side of Leitch-Smith's spot-kick for Vale.
But Richard Duffy missed his penalty, which swung the shoot-out in Albion's favour. McManaman, Fletcher and Chester converted from 12 yards to ensure Albion's progress into the next round.
ALBION: Myhill, Chester, McAuley, Olsson, Brunt (Dawson 12), Gnabry (McManaman 57), Yacob, Fletcher, McClean, Lambert, Ideye (Rondon 57). Subs: Rose, Gardner, Sessegnon, Anichebe.
BOOKINGS: Dawson (foul 61), McAuley (foul 73), McManaman (simulation 113)
PORT VALE: Alnwick, Purkiss, Dickinson, Duffy, Inniss, Grant, Foley, Andoh (Daniel 94), Moore, Dodds, Ikpeazu (Leitch-Smith 67). Subs: Johnson, Birchall, Streete, Brown, Kelly.
BOOKINGS: Ikpeazu (foul 60), Duffy (foul 76), Foley (foul 98), Alnwick (unsporting behaviour 116)
Lambert: Scores. 1-0
Leitch-Smith: Scores. 1-1
Yacob: Scores. 2-1
Duffy: Misses. 2-1
McManaman: Scores. 3-1
Purkiss: Scores. 3-2
Fletcher: Scores. 4-2
Foley: Scores. 4-3
Chester: Scores. 5-3
STAR MAN: Lambert