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Gunners edge Baggies on penalties
Arsenal's winning streak continued as they defeated West Brom on penalties at The Hawthorns to book their place in the Capital One Cup fourth round.
Albion - whose first XI featured eight changes and their opponents' nine - had the best chances of the first half, with a Craig Dawson header being pushed over by Lukasz Fabianski.
There was also Steven Reid's free-kick, seemingly sent over by a slight touch of Fabianski's glove, although the goalkeeper argued he had not made contact, hoping to prevent a corner that was given nonetheless.
There was no question that Fabianski had produced a save, and a good one, to keep out Youssouf Mulumbu's strike on the hour mark.
And a minute later Arsenal had the lead as Mulumbu lost possession, Bendtner slipped in Thomas Eisfeld and the 20-year-old German midfielder slotted in what was his first Gunners goal on his maiden start.
West Brom equalised in the 71st minute when Saido Berahino, scorer of a hat-trick in round two, headed past Fabianski from close range.
Baggies substitute Morgan Amalfitano hit the bar in extra time but the teams could not be separated over 120 minutes.
In the shoot-out, West Brom initially had the advantage after Luke Daniels saved Serge Gnabry's effort, but misses from Dawson and Amalfitano allowed Nacho Monreal to seal victory for the away side.
Arsenal, who have now won eight successive matches in all competitions, will host Chelsea in round four.
West Brom created an opening early on as Shane Long got his head to skipper Reid's cross, the ball then striking Carl Jenkinson and diverting to Fabianski.
Five minutes later Bendtner missed Ryo Miyaichi's delivery and collided with the post, continuing afterwards having briefly received treatment.
Albion began to settle and after Graham Dorrans shanked an effort, his corner was headed goalwards by Dawson and Fabianski tipped over the bar.
Isaac Hayden might have felt lucky to escape with only a booking for his tackle on Mulumbu in the 33rd minute, and Monreal also received a yellow card moments later for fouling Berahino, with Dorrans then blasting the resulting free-kick wide.
The visitors looked to apply some pressure towards the end of the half and after a Monreal shot was blocked, there was a scare for West Brom when Daniels slipped as a corner came into the box, but they managed to clear the ball.
The Baggies went close just prior to the interval as Reid's free-kick whistled over - via a touch from Fabianski according to the match officials, despite the Poland stopper's claims to the contrary.
Eisfeld looped a shot over the bar shortly into the second half, and Thomas Vermaelen then became the third Arsenal player to receive a yellow card, having felled Long.
Albion stepped things up a gear and Per Mertesacker intervened to clear a Long cross, with Fabianski then diving to excellently palm behind Mulumbu's drive from the edge of the box.
Moments later, though, Mulumbu gave the ball away and Arsenal took advantage as Eisfeld latched on to Bendtner's through-ball to finish.
Berahino came to West Brom's rescue, nodding in from Long's tee-up to draw things level.
Berahino then flashed a shot over, before Diego Lugano picked up the hosts' first booking for a two-footed challenge on Mertesacker.
Extra-time was confirmed after no Arsenal player was able to get a killer touch on Jenkinson's late delivery into the danger zone.
A deflected Miyaichi effort almost caught out Daniels and Dawson then made a superb last-ditch tackle to take the ball from Bendtner, who was through on goal.
Arsenal substitute Chuba Akpom drilled a shot across the face of goal just before the extra-time break, and just after the interval, Albion substitute Markus Rosenberg saw Fabianski turn his effort behind.
Another Arsenal substitute, Hector Bellerin, tried his luck with two shots, one saved by Daniels and the other going wide.
Amalfitano crashed the ball against the bar, Rosenberg was denied once again and Scott Sinclair passed up a good-looking opportunity.
The contest duly went to penalties and Monreal had the final say after Dawson and Amalfitano's failed attempts.