Alastair Cook's side ended a run of 10 Test matches without victory at the Ageas Bowl on Thursday, Anderson returning match figures of 7-77, his best of the series to date.
Strong performances from England's batsmen helped set up the victory before Anderson and Moeen Ali shone with the ball, the latter taking 6-67 in India's second innings.
Relief was etched all over the faces of the hosts as they celebrated a first Test triumph under new coach Peter Moores, and Anderson thinks the success could prove a catalyst for future improvement.
"I think it has just started to turn a corner, I'm hoping," he told the ECB's official website. "It didn't really start that well for us [England's home international season] – we lost the one-day series and Test series against Sri Lanka and we were 1-0 down after two Tests against India.
"It wasn't a great start for us even though we didn't play particularly badly.
"Now after the Test at the Ageas Bowl I thought we certainly turned a corner.
"It was a very good performance from us and something that I hope we can kick on from and use to produce some better form throughout the summer."
Old Trafford, Anderson's home ground, will host the fourth Test, which gets underway on Thursday.
Anderson is set to be available for selection after being found not guilty of a Level 3 offence by an International Cricket Council judicial commissioner following his alleged altercation with Ravindra Jadeja during the series opener at Trent Bridge.
However, ICC chief executive David Richardson could yet choose to appeal the verdict.