Albion's Holland Under-21 international striker Sherjill MacDonald missed the penalty that handed Middlesbrough victory on penalties for the second successive round having also won a shoot-out against Bristol City.
Middlesbrough's Stewart Downing and Albion's Jonathan Greening both converted the first two spot-kicks before Dong-Gook Lee hit the post and Neil Clement blazed over the bar.
James Morrison, Darren Carter, Julio Arca, Paul Robinson, Yakubu, Diomansy Kamara and George Boateng scored before MacDonald blazed over the bar to hand Boro victory.
The two teams could not be separated after 120 minutes with Carter's first-half opener being cancelled out by Mark Viduka's 62nd minute strike.
Middlesbrough failed to make the most of a one-man advantage for the final 27 minutes of extra-time after striker Nathan Ellington had been sent off for his challenge on Stuart Parnaby.
Carter had fired Albion into a deserved lead after Middlesbrough were outplayed in the opening period when only the heroics of goalkeeper Brad Jones kept them in contention.
But Albion could not keep up the same level of intensity after the break and an improved Middlesbrough drew level through in-form Viduka's 12th goal of the season and his ninth in 11 games.
Boro had been building up a head of steam before Viduka struck with Emanuel Pogatetz just failing to convert a corner from Downing, who was himself then denied by Dean Kiely.
But there was nothing that Kiely could do to stop Viduka's smart piece of finishing.
Just like Albion's goal it was created on the right wing with George Boateng picking out substitute Parnaby.
Parnaby's first-time cross was controlled superbly by Viduka before the former Leeds United striker fired past the wrong-footed Kiely from 16 yards.
Boro were transformed once they were back on level terms and they were unlucky not book their quarter-final place in normal time.
While Jones had kept Albion at bay in the first half, it was Kiely who starred after the break denying both Yakubu and Lee in a frantic closing spell.
Middlesbrough could count themselves lucky to last as long as they did before falling behind as it was purely due to Jones that they were not trailing before Carter struck.
Jones, who was in the side after first-choice Mark Schwarzer was ruled out with a back injury, single-handedly kept Albion at bay.
The Australian first denied Richard Chaplow before tipping a header from Paul McShane over the bar.
Jones also frustrated Ellington and Zoltan Gera before his resistance was broken.
This time there was nothing he could do after Jason Koumas and Ellington combined to set-up Carter.
Koumas picked out Ellington with a cross-field pass and the former Wigan striker rolled the ball into the path of Carter who surged forward before unleashing a low 20-yard drive that left the stranded Jones rooted to the spot.