Having played out encouraging 1-0 defeats against Aston Villa and Liverpool, the south coast side, led by Callum Wilson's hat-trick, were irresistible at times at Upton Park.
Howe's side attacked with a refreshing enthusiasm and effervescence and looked capable of scoring at will.
Having started the day in the relegation zone -- without a point or goal to their name -- Howe said the victory would instil a belief in his players that they are capable of competing with any team in the Premier League.
"(Getting the first points) means everything," Howe told Sky Sport. "We really needed this today.
"Not in terms of the league table or any nonsense like that but just for our own belief that we can go anywhere and compete.
"We've done that in the two games we've had already and come up with nothing but it was important today we backed it up with the result.
"We were excellent in the first half and a real threat on the counter-attack. We were very dynamic, passed the ball well and created numerous opportunities.
"At 2-2 it would have been easy to buckle but we came back again and I thought we thoroughly deserved the win."
While Bournemouth troubled the hosts every time they went forward West ham contributed to their own downfall.
Wilson's second goal came after he capitalised on poor control from Aaron Cresswell -- who was also caught out of position in the build-up to the opener -- while his hat-trick goal came from the spot after Carl Jenkinson fouled Max Gradel.
Having fought back to 2-2, however, West Ham manager Slaven Bilic said his side didn't show enough desire to win despite appearing to have gained the momentum.
"It's not an alarming situation but we can't continue to play without more desire," the Croatian told the BBC. "We simply need a better mentality."
"It went wrong from the start. We played a very bad first half. It is very hard to explain three of their four goals, you can't make errors like that at this level."
(Reporting by Tom Hayward; Editing by Ken Ferris; editing by Ken Ferris)
Share
