Howe made 10 changes to his starting XI after an 8-0 win over Birmingham City in the Championship in midweek but the changes did not halt their momentum as they moved into the quarter-finals of the competition for the first time.
Eunan O'Kane put Bournemouth ahead just after half-time at the Goldsands Stadium, before West Brom equalised when Georgios Samaras' shot deflected in off Tommy Elphick for an own goal.
But Callum Wilson popped up moments later to score the winner, and Howe said it was deserved reward for his hard-working outfit.
"It was a great performance right from the start," Howe told Sky Sports.
"I thought we passed the ball really well, I think the main feature was our hard work, our discipline. We restricted them to few chances, and against quality players like that, I think that's no mean feat.
"The first one's a real quality goal. I thought Junior Stanislas played a key role in it with some excellent footwork. It was a really good driving run by Eunan, and an excellent finish...we felt one might be enough, we felt like we might just hang on there, they had a bit of pressure at the end and of course we disappointed with the unfortunate own goal.
"But we showed real strength of character to go up the other end and score straight away, and I think that's the most pleasing aspect of tonight."
Howe said he had full confidence in his squad to fly the flag for the club, despite wholesale changes from their rout in Birmingham.
"We always felt we had a really strong squad. Early season we were finding ways not to win games," Howe said.
"We were so dominant in our performances, a couple of results got away from us. But I think the recent run of results shows strength in depth we have.
"And obviously today, [I was] able to make 10 changes and I didn't feel I was weakening the team.
"The lads have been on such a good run I haven't wanted to tinker too much with the team but we have really good players here."
West Brom boss Alan Irvine said some of his players wasted an opportunity to secure a more permanent first-team spot, and added their concession of goals came down to loose possession and poor decision making.
"Very disappointed. This was an opportunity for a number of the players, who have been hoping to get selected, to impress and to stake a really strong claim for a starting place," Irvine told Sky Sports.
"Some of them did but not enough of them.
"The first one wasn't [West Brom switching off]. The first one came from us giving the ball away unnecessarily in the middle of the park. The second one was, in terms of probably a couple of poor decisions, positional decisions. And we got punished for it."
