First-half goals by new boy Albert Riera and Andy Cole and a strike in the second period from Darius Vassell made it six Premiership games without a win for Newcastle.
While the Tyneside team remains in the lower reaches of the table, City halted their own slide to mid-table as they registered only their second win in seven League games.
And it was a night when wantaway midfielder Joey Barton produced a masterful performance to silence the boo-boys.
Barton, who on Monday requested a transfer after rejecting a new contract, was jeered when the teams were announced, and in the early part of the match.
But after setting up City's first goal in the 14th minute he won back favour with many of the fans.
Barton whipped over a cross from the right which was cleared by Jean-Alain Boumsong only as far as Riera who fired home an unstoppable shot from the edge of the penalty area.
City, who threatened a brittle Newcastle defence every time they attacked, deservedly doubled their lead in the 38th minute.
Newcastle's defending was awful as Kiki Musampa played the ball in to Vassell and his delightful chip was headed home by Cole for his tenth goal of the season.
It was a measure of Souness' desperation that he made two half-time substitutions bringing on Nolberto Solano and Albert Luque for Charles N'Zogbia and Michael Chopra.
But it failed to change Newcastle's fortunes as they conceded a third goal in the 62nd minute.
Solano gave the ball away near the City box, and the home side broke swiftly upfield with Cole releasing Vassell who out-paced Boumsong before slotting the ball low past keeper Shay Given, for his eighth goal of the season.
With victory assured City brought on new £6million striker Georgios Samaras midway through the second period for his debut.
City had chances to have won by an even wider margin, most notably when Trevor Sinclair was denied by a super stop from Given.
Towards the end there was a mixture of boos and cheers when Barton was replaced by Micah Richards. But at the final whistle City celebrated an important victory while Newcastle lamented on another costly defeat.