After s 20-year-old German starlet, Thomas Eisfeld gave the away side the lead in the second half, latching onto a perfectly weighted through-ball from Nicklas Bendtner, before the Baggies responded through Saido Berahino.
But with the scores still level after extra-time, the match went to a penalty shoot-out. Serge Gnabry was the first player to miss, giving West Brom the advantage, but Craig Dawson and Morgan Amalfitano both failed to beat Lukasz Fabianski as Monreal converted the final penalty to win the tie.
Steve Clarke made eight changes to the side that beat Sunderland 3-0 on Saturday, with only Youssouf Mulumbu, Scott Sinclair and Stephane Sessegnon retaining their places.
Arsenal too took the opportunity to rest key personnel, with Per Mertesacker and Serge Gnabry the only survivors from the 3-1 win over Stoke City, while Bendtner made his first start for the club in two years.
West Brom had the first chance in the 25th minute when Dawson's looping header from Graham Dorrans' corner required Fabianski to tip over the crossbar. Arsene Wenger's side were then lucky not to have 18-year-old debutant Isaac Hayden sent off. The midfielder’s sliding tackle on Mulumbu was late and robust but referee Robert Madley deemed it only a yellow card.
Bendtner could have wrapped it up in the 97th minute when Serge Gnabry sent him racing clear, but the Dane took too long to get his shot away and allowed Dawson to recover and make a last-ditch tackle.
And with just four minutes remaining, substitute Amalfitano thought he had won it for West Brom but saw his drilled effort cannon back off the bar. Markus Rosenburg went close moments later, before Sinclair sliced a volley well wide from close range.
That meant the match headed to penalties where, after two successful spot-kicks for the hosts and one for the away side, Gnabry saw his effort saved.
But Dawson and Amalfitano both fired wide for the home side, leaving Monreal the chance to win the tie, and the Spaniard made no mistake as he fired high into the roof of the net to set up a fourth round clash with Chelsea.