By Chris Harris at the Hawthorns
Arsenal are through to the fourth round of the Capital One Cup after a dramatic penalty shoot-out victory on Wednesday night.
But West Brom responded well and levelled 10 minutes later through Saido Berahino's close-range header.
Bendtner had a chance to win it in extra time when he was put through by Serge Gnabry, while Steven Reid and Morgan Amalfitano hit the crossbar for West Brom.
Ultimately, two hours of football could not separate the sides so the tie went to spot-kicks.
Reid, Bendtner and Markus Rosenberg all scored before Luke Daniels saved from Gnabry. James Morrison and Kris Olsson netted but Craig Dawson missed and Chuba Akpom levelled the shoot-out.
The tie swung Arsenal's way when Amalfitano shot wide - and Nacho Monreal found the top corner to take the Gunners through.
It was a compelling end to a slow-burner of a tie and Arsenal's reward is a London derby against Chelsea.
For now, they can revel in this memorable win on a night of guts and glory.
There was one surprise in Arsène Wenger's line-up with expected starter Mathieu Flamini left on the bench. The Frenchman was there as a precaution after picking up a minor shoulder problem.
Otherwise it was the usual League Cup mix of steady pros, fringe players and exciting young talent. A reassuring spine was in place with captain Thomas Vermaelen partnered by Per Mertesacker and Mikel Arteta in front of them. Flamini's injury handed a debut to Isaac Hayden while Eisfeld and Ryo made their first starts for the Club.
There was also a notable comeback with Bendtner pulling on an Arsenal shirt for the first time since August 2011.
With so many changes and so many new combinations on the pitch, perhaps it was no surprise that Arsenal lacked cohesion in an uneventful first half.
With Stephane Sessegnon dropping off and finding space in between the lines, and Berahino's pace testing Monreal, West Brom were a threat.
The half-chances, when they came, were Albion's. After 23 minutes Sessegnon tricked his way past Jenkinson on the left and stood up a cross to the back post. The ball bounced invitingly for Graham Dorrans but he smashed it high and wide.
Dawson was the next to have a sniff of goal, getting in front of Hayden to loop in a header which Fabianski tipped over.
Arsenal threatened sporadically with Jenkinson making three positive forays down the right, but perhaps the visitors' best opening of the half came when an innocuous Gnabry corner missed everyone and squirmed across the six-yard box.
Dorrans wasted a free-kick at the other end but West Brom were inches away with another set-piece in first-half stoppage time when Reid's dipping effort clipped the top of the crossbar.
It was an exciting end to a humdrum first period and it set the tone for the rest of the tie.
Within two minutes of the restart Arsenal fashioned their best chance so far. Jenkinson, impressively proactive, picked out Eisfeld on the edge of the box. The young German had time to measure his finish but leaned back and fired over.
Then it was Arsenal's turn to enjoy a let-off. Goran Popov delivered a fine cross from the left, Berahino steadied himself for a free header at the far post - and promptly lost his footing.
Unabashed, West Brom pressed forward. Mertesacker, a towering presence at the back, made a critical intervention as Berahino crossed from the right. And Fabianski showed fine reflexes to tip away Youssouf Mulumbu's fearsome drive on the hour mark.
Within a minute of the Pole's brilliance, Arsenal were ahead. A slick move found its way to Bendtner on the edge of the box and the Dane slipped a pass through to Eisfeld, who finished clinically.
Suddenly the game opened up with West Brom pushing men forward and Arsenal looking threatening on the counter-attack. Gnabry almost found space for a shot as the visitors looked to wrap up the tie - but they were pegged back 10 minutes after going ahead.
A corner was half-cleared beyond the far post and Long clipped the ball back across goal for Berahino to dispatch a powerful header past Fabianski.
The home side looked strong but, with Mertesacker and Vermaelen in tandem, Arsenal repelled them, dealing with cross after cross. At the other end Gnabry cut inside before firing wide with his left foot as the visitors broke sporadically.
Arsenal had one more chance to win it in normal time, substitute Akpom and Gnabry both sliding in to meet Jenkinson's cross - and both missing by inches.
And so to extra time.
Arsenal continued to defend stoutly and their best chance fell to Bendtner, who was played through by Gnabry six minutes into the first period. A fully-fit Bendtner might well have scored but Dawson made up ground and executed a perfect challenge as the Dane shaped to shoot.
Akpom fired wide before the teams changed ends and another sub, Hector Bellerin, tried his luck twice in the second period. West Brom went even closer when Amalfitano clattered the crossbar.
It came down to penalties - as it did in Arsenal's last Capital One Cup tie. That brought ignominy at Bradford last December… but this one had a happy ending.
Reid found the top corner and Bendtner the bottom corner before Rosenberg scored and Gnabry was foiled by Daniels.
Morrison consolidated Albion's advantage and Olsson beat Daniels to keep Arsenal in the hunt.
Dawson sliced his penalty wide and, after Akpom levelled and Amalfitano missed, Monreal stepped up to find the roof of the net and take the Gunners through.
- Monreal Yellow Card
- Vermaelen Yellow Card
- Eisfeld 82 Goal!
- Hayden 84 Yellow Card
- Arteta 95 Yellow Card
- Bellerin 95
- Akpom 82
- Olsson 84
West Bromwich Albion
- Lugano Yellow Card
- Reid Yellow Card
- Popov Yellow Card
- Mulumbu 90
- Long 90
- Berahino 100 Goal!
- Amalfitano 100
- Morrison 90
- Rosenberg 90