Albion set up an all Premier League tie in the League Cup third-round with Norwich after beating Port Vale on spot kicks.
The Baggies were unable to find a way pas Ben Alnwick in the visitors goal with Brown Ideye, Rickie Lambert and Salomon Rondon all coming close to breaking the deadlock.
Tony Pulis stayed true to his word and picked a strong side against League One Vale.
James Chester, Serge Gnarby, plus Lambert and Ideye were just four changes to the side that faced Chelsea.
The front pair combined for Albion’s best chance of the first half when Lambert crossed for Ideye to head inches wide.
Lambert saw an ambitious 40 yard volley palmed over after the break before Salomon Rondon came off the bench to head against the cross bar.
Neither team could find a goal in extra time and James Chester scored the winning penalty for Albion after the visitors had twiced missed from the spot.
Afterwards, Pulis praised the contribution of substitute Rondon – despite him missing several chances.
"He will score goals, I'm convinced about that."
"Salomon came on and could've scored four goals - he made some great runs but he's just been a bit unfortunate.
"We didn't want to give him too much game time having flown in just and he's getting used to the country.
"Twenty minutes would have been ideal for him but he'll now get plenty of rest."
Can the Baggies beat Norwich in the next round? Have your say at Baggies Banter.