Manager Nigel Adkins was relieved to see Southampton finally get their first home win of the season against Bournemouth.
Rickie Lambert struck twice from the penalty spot to earn Saints the south-coast bragging rights at St Mary's.
"It's great to have our first win at St Mary`s, a clean sheet and a 2-0 victory against our local rivals who are flying high," said Adkins.
"I thought we were comfortable in the first 15 minutes and the game should have been dead and buried.
"We are trying to improve all the time, and while we want to play good football, we are also learning there is more than one way to win a game and winning is the most important thing."