Schneiderlin fired the visitors into a third-minute lead with the Magpies sluggish in the early stages, and it took half an hour for them to restore parity when Moussa Sissoko applied the finishing touch to a flowing move involving compatriots Yohan Cabaye and Yoan Gouffran.
However, it was Papiss Cisse who took up the baton three minutes before the break when keeper Rob Elliot's clearance sat up nicely for him 30 yards from goal and he lashed it past helpless keeper Artur Boruc off the underside of the crossbar.
However, Cisse's thunderbolt was not to prove decisive and Rickie Lambert, who had already forced a fine save from Premier League debutant Elliot, levelled from Adam Lallana's 50th-minute cross.
The Magpies restored their lead with 67 minutes played after referee Chris Foy, perhaps harshly, awarded a penalty against substitute Danny Fox when he blocked Mathieu Debuchy's volleyed cross with his arm, and Cabaye duly obliged from the spot.
There was further misfortune for Fox 11 minutes from time when his attempted clearance struck team-mate Jos Hooiveld and flew past Boruc into the net, and the points were safe.
Former Saints boss Alan Pardew was hugely impressed with the performance of Mauricio Pochettino's men, and is convinced they will remain in the Premier League next season.
He said: "They are a good team - they won't go down, no way."
His confidence is shared by Pochettino and goalscorer Schneiderlin.
The midfielder told the club's official website: "We didn't try to get too carried away when we won against Manchester City, and today we will not get too down about losing in Newcastle.
"That's football and sometimes you have an off day. I don't think we had an off day, but we lost the game and now we need to bounce back.
"We are very confident that we can avoid relegation, and I think we will, but it's by bouncing back and having a good performance against QPR."