Gylfi Sigurdsson proved to be the matchwinner in the fifth minute of extra-time, just moments after Brian Howard's strike in the third of four stoppage-time minutes at the end of normal time had brought a dramatic end to the fifth-round replay.
It proved to be an historic night for Reading, with their first win at The Hawthorns since 1995 securing their place in the last eight for the first time since 1927.
But it could have been so different for a shell-shocked Albion side who looked destined for their second quarter-final place in three seasons.
The most relieved man in the Black Country must surely have been Royals goalkeeper Adam Federici, whose calamitous 47th-minute gaff in letting Robert Koren's shot squirm horribly through his body looked to have proved the difference.
Koren had earlier handed the Baggies a sixth-minute lead in the fifth-round replay before Jimmy Kebe levelled almost immediately - both players also scored the first two goals in the initial 2-2 draw between the two sides at the Madejski Stadium.
The final whistle was greeted by a mass melee involving players, stewards and officials, with a Reading player appearing to be shown a red card.
Slovenia captain Koren had already twice gone close when he opened the scoring after just six minutes.
Roman Bednar received the ball 25 yards out and his low drive was parried by Federici, with Ryan Bertrand clearing Luke Moore's rebound off the line.
But the Royals full-back could only send the ball straight into the path of Koren who finally found the net at the third time of asking.
But Albion's lead did not last long as Kebe, who scored after nine seconds in the first meeting, side-footed home from six yards after Scott Carson had failed to keep hold of Jay Tabb's low shot across the face of goal in a rip-roaring start to the tie.
But the frenetic opening 15 minutes was as good as it got in the first half, with no real goalmouth action of note in the remaining half hour.
Yet the 13,985 inside The Hawthorns were treated to a second-half opening similar to the first although this time Albion took just two minutes to find the net.
And they did so in hugely fortuitous fashion.
Youssouf Mulumbu found Koren and he turned on the edge of the area before firing a low shot that went straight through Federici's grasp and into the back of the net.
Reading, however, almost repeated their first-half feat but Sigurdsson's dipping long-range effort came back off the crossbar.
The Iceland Under-21 international was presented with a second opportunity to level the tie in the 69th minute after Gabriel Tamas's mistake but he could only fire straight at Carson.
An ordinary final 20 minutes followed with West Brom seemingly destined for a place in the last eight, that was until Howard silenced the home crowd in the third minute of stoppage time.
And there was worse to come for Albion in extra-time as Sigurdsson settled matters with a sublime curling effort from 25 yards - ensuring West Brom were added to Reading's list of scalps in this season's competition, with the Royals having already seen off Liverpool and Burnley.
The referee later confirmed Jobi McAnuff was the Royals player dismissed for violent conduct after the final whistle.