West Brom needed penalties to beat League One side Peterborough United following a 1-1 draw in the fourth-round replay at London Road on Wednesday.
Ben Foster saved spot kicks from Martin Samuelsen and Lee Angol as Tony Pulis' side edged the shootout 4-3, Darren Fletcher having missed for West Brom.
Jon Taylor scored one of Peterborough's two late equalisers in the first game at The Hawthorns and he put his side ahead after 54 minutes, shooting low across Foster.
Fletcher levelled the scores after 71 minutes, smashing home after sustained West Brom pressure as the visitors sought to avoid an embarrassing exit to lower-league opposition.
Foster's efforts in denying teenage midfielder Samuelsen and 21-year-old striker Angol earned West Brom a trip to Championship club Reading in the fifth round on February 20.
Former Peterborough loanee Saido Berahino started for West Brom, while the hosts' Gabriel Zakuani made his first start since November after recovering from hamstring surgery.
Peterborough began the game well on top and excellent close dribbling from Samuelsen led to Harry Beautyman having a shot blocked after five minutes, before Foster made saves from Taylor and Chris Forrester.
West Brom had failed to register a shot on target in three of their last four league games, but they mustered an accurate effort after 25 minutes when Ben Alnwick smothered Craig Gardner's low free-kick.
Berahino went close to scoring the opening goal after 35 minutes when Salomon Rondon knocked down a long ball for his strike partner, who cushioned a drive just over the angle.
West Brom should have taken the lead five minutes before half-time, but James Chester, arriving late at the back post, could only aim his shot straight at team-mate Fletcher.
Peterborough had been by far the better side and the League One team took a deserved lead after 54 minutes when Angol broke at pace and fed Taylor, who shot across Foster and into the bottom corner via a small deflection off Chester.
West Brom knocked Peterborough out of the FA Cup in 2008 and 2009 but they almost fell further behind after 68 minutes when Gardner hooked a loose ball over his own crossbar.
Moments later Gardner almost scored at the correct end, fizzing a sensational volley just wide, and with the visitors cranking up the pressure they scored a fantastic equaliser after 71 minutes.
James McClean's cross was cleared straight to Fletcher and the midfielder hammered a wonderful half-volley high into the net.
West Brom almost scored the winner with just four minutes to go when Alnwick hastily raced off his line, but Michael Bostwick got back brilliantly to clear Berahino's shot away from danger.
Alnwick then saved with his legs from Rondon in the final minute of normal time.
Samuelsen opened up the West Brom defence with a glorious run eight minutes into extra-time, but his shot was over the crossbar, before Rondon's 20-yard drive flew just wide of the post.
Substitute Marcus Maddison almost settled the tie with an audacious stroke of genius with minutes of addition time remaining, but his chip floated just over Foster's crossbar.
Zakuani then put his body on the line to block Gardner's volley on the line and Berahino should have won the match in the dying moments but headed wide.
Sebastien Pocognoli, Berahino, Gardner and Chester all scored from 12 yards for the visitors, but Foster was West Brom's hero in the shootout, saving from Samuelsen and Angol, to spare the Premier League side's blushes.
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