Sam Allardyce's charges have lost just once to the newly promoted side in their last seven encounters, while the Welsh outfit reached the final of this competition in 2012
Malky Mackay's side lost 2-0 at Upton Park on the opening day of the Premier League season after goals from Joe Cole and Kevin Nolan, but the Welsh club have seen an upturn in fortunes since that early setback.
Cardiff bounced back with a stunning 3-2 defeat of Manchester City in their first ever Premier League home game before claiming credible draws with Everton and fellow promoted side Hull City, but they go into this game on the back of a 1-0 defeat to Tottenham on Sunday, which was sealed by Paulinho's stoppage-time winner.
Progression to the third round was sealed with a 2-0 win at Accrington Stanley last month, as goals from Nicky Maynard and Rudy Gestede saw a much-changed side safely through.
Mackay will be hoping for a repeat of his side's League Cup heroics two years ago. Cardiff emerged victorious from penalty shootouts in both the third round and the semi-final before finally succumbing on spot-kicks after a 2-2 draw with Liverpool in the final at Wembley.
West Ham, beaten Capital One Cup finalists against Liverpool in 1981, booked their place in the third round with a less than convincing 2-1 home win over League Two side Cheltenham Town.
Ricardo Vaz Te and Ravel Morrison were on the scoresheet that evening, but goals have been hard to come by since then, with Sam Allardyce's side failing to find the net in three of their four Premier League games following their opening-day defeat of Cardiff.
They have taken points from goalless draws in two of those matches but, like Cardiff, were undone by a late winner in their last league fixture as Romelu Lukaku gave Everton a 3-2 win at Upton Park on Saturday.