It was also the first win under new manager Sam Allardyce, who replaced Dutchman Dick Advocaat just eight games into the season.
Sunderland have now made it six consecutive derby wins over Newcastle and Jones, who scored the game's second goal, said he hoped the win would give his team some much-needed momentum.
"It's huge for us. It's a derby game, so you want to win to make it six in a row. You want to do it for the fans, do it for the club and have the bragging rights," Jones was quoted as saying by the British media.
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"But to get our first win of the season is massive and we needed to get that pressure off ourselves.
"It's there for everyone to see, when you look at the league, everyone is talking about it.
"Hopefully now we've got that first win, we can move onwards and upwards, and get three points next weekend against Everton," the 28-year-old Englishman added.
Sunderland will hope to get out of the relegation zone when they travel to face an out-of-sorts Everton on Sunday.
Following Sunday's defeat by Arsenal, the Merseyside club have now failed to win their last three league games.
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Sudipto Ganguly)
