The Cherries had lost their first four games of the Premier League campaign but goals from Andrew Surman and Jermain Defoe helped them come from behind against their south coast rivals at the Vitality Stadium.
When asked about the result after the match, Howe told BBC Sport: "A lot of emotions, relief is probably the biggest one. We have had a tough run of fixtures and today was really important.
"[Brighton] played deep, they were compact and we knew it would be difficult. The two goals have given everyone a confidence lift."
Up next for the 19th-placed Cherries is an EFL Cup third-round home tie against the Seagulls on Tuesday before returning to Premier League action at Everton next Saturday.