The result allowed Sale to leapfrog Leicester in the Premiership table and move up to fifth ahead of Saturday's crunch trip to Harlequins.
Saint-Andre's men need to win their remaining two games to secure a play-off spot and the showdown at the Stoop will pose a far sterner test.
Saint-Andre, who singled out full-back Ben Foden for special praise, said: "We've got 59 points and we're fifth so we've just got to keep going and beat Harlequins and London Irish the following week.
"We could have players back for next week - the likes of Jason White and Sebastien Chabal - but it will be a tough game at Harlequins.
"The Guinness Premiership is so tight this year but it's very exciting as well and I've never known a season like it."
Foden, meanwhile, has agreed to join newly-promoted Northampton for next season but Saint-Andre backed him to earn a call-up to the England squad for the summer tour of New Zealand.
Saint-Andre added: "He was the best player on the pitch and he deserves to go on the summer tour of New Zealand with England."
Centre Chris Bell opened the scoring in the second minute and completed his brace in the 17th minute to sandwich a try from rookie wing Selorm Kuadey.
Juan Martin Fernandez Lobbe added a fourth shortly before half-time to secure a bonus point and claimed his second after the break before further scores from Will Cliff, Foden and Michael Hills took Sale's try tally to eight.
Newcastle - missing England quartet Jonny Wilkinson, Mathew Tait, Jamie Noon and Toby Flood through injury - struggled badly as they slid to their seventh successive Premiership defeat.
Acting director of rugby Steve Bates said: "Apart from a few daft mistakes in the first half I thought we put up a really spirited effort.
"I'm really proud of the lads in terms of the commitment they showed.
"You look at their pack and we knew it was always going to be a tough game, but I was generally pleased with the effort.
"Some of the stuff we did was very pleasing and it was far from dispiriting."