The first half began with an error from both goalkeepers, as Brad Jones spilled a cross and allowed West Brom to take the lead through Gabriel Tamas before Ben Foster let a speculative Nuri Sahin shot squirm past him for the equaliser.
The second period was similarly frantic, and it took until the 82nd minute for the deadlock to be broken, as Sahin swept home his second to give the Reds the victory.
West Brom went with a strong side as they looked to continue their progress through the competition, with summer signing Markus Rosenberg given a full home debut.
|6/1||Nuri Sahin is 6/1 with William Hill to score anytime when Liverpool take on Norwich City
The game started badly for the away side, and they found themselves behind in just the third minute. A free kick came into the Liverpool box, and was spilled by goalkeeper Brad Jones directly into the path of Gabriel Tamas, who drove the ball home comfortably.
It could have been worse for the Reds just a couple of minutes later, as Romelu Lukaku wrestled his way through their defence, but his shot was deflected behind by Jamie Carragher.
The away side struggled to get out of their half for much of the opening exchanges, but then saw Yesil put a free header wide of Ben Foster’s post after a superb Oussama Assaidi cross from the left.
Liverpool were beginning to play with more confidence, and were rewarded for their enterprise in the 15th minute by another goalkeeping error, as Ben Foster allowed Nuri Sahin's long-range strike to squeeze past him for the equaliser.
The away side then began to take control of the game, and were by far the better team whilst not creating more goalscoring opportunities, with Assaidi in particular enjoying a great deal of freedom on the left.
However, neither side was able to create any further chances meaning the first half ended honours even.
The second period began frantically, with both sides having glorious chances as Stewart Downing missed a free header from a cross and Lukaku again wreaked havoc in the opening moments.
In the 49th minute, the Reds were almost gifted another goal, as Foster punched a vicious Yesil shot through his own legs and was fortunate to see it bounce over the bar.
However, the Baggies also had some good moments of their own early in the half, with Rosenberg forcing a good save from Jones with a shot from just outside the penalty area.
The game then descended into a similar pattern to that of the first half, with Liverpool enjoying more of the possession but with neither side able to create any clear chances, and struggling to move the ball beyond a congested midfield.
The Reds then had perhaps their best chance of the half in the 73rd minute, as Sebastian Coates flicked a dangerous free kick towards the goal, and was denied only by a reflex stop from Foster in the Baggies goal.
Liverpool then made history with the introduction of Jerome Sinclair, who became their youngest-ever first-team player at the age of 16 years and six days when he came on in the 80th minute.
Just two minutes later, the Reds were celebrating again, as after some superb passing and movement, Sahin was on hand to sweep the ball home and give the away side a 2-1 lead.
And, despite some nervy moments as West Brom pumped the ball long, the Merseysiders held on for the final few minutes to advance to the next round.