The Championship club racked up their record Football League win on the weekend, demolishing Birmingham City 8-0 at St Andrew's.
Another club milestone is now in Bournemouth's sights as Alan Irvine's side make the trip from the Midlands.
Bournemouth have reached this stage of the League Cup just twice in their history - in 1961 and 1963 - and are yet to make the fifth round.
Howe believes the confidence coursing through the squad leaves them in peak condition to spring an upset.
"It's always nice and we have done it [made history] several times in the last few years," he told BBC Radio Solent.
"They are really nice milestones because you don't set out to achieve things like that.
"But when they happen, hopefully someone will be talking in 50 years' time about this team. That's always nice to think about.
"I know that [West Brom] have approached the game very seriously - they've watched us several times so they'll know all about our strengths and weaknesses.
"It'll be a great game. In the cup games they're free games for us away from points and the pressure of the league. We're forced to make some changes so we'll try and give West Brom a game."
Harry Arter and Steve Cook picked up their fifth bookings of the season against Birmingham, which will prevent Howe from naming an unchanged side, but striker Yann Kermogant is back from a three-match ban to boost his options.
Bournemouth have won six of their last seven matches, but West Brom enter the game in decent form themselves, and displayed all their battling qualities to rescue a 2-2 draw with Crystal Palace on Saturday.
Saido Berahino's late penalty secured a point after Irvine's men had gone 2-0 down in the first half and West Brom have lost just one of their last six games.
Two last-gasp goals in the previous round overturned a 2-1 scoreline in Hull City's favour to secure progression, after Irvine had made 11 changes to his team.
The Scot may be wary of doing so again versus a club in such form and the continued absences of Jonas Olsson (Achilles), Silvestre Varela (groin) and Claudio Yacob (personal reasons) may prevent him from making too many alterations.
Ben Foster returned from a calf injury to face Palace, but is expected to make way for back-up goalkeeper Boaz Myhill.
Reaching the fifth round would equal West Brom's best effort in the League Cup over the past decade - they last went as far in 2010-11 before defeat to second-tier opposition in the form of Ipswich Town.
