Gundogan gave City the lead in a low-key game on Sunday (AEDT) with a close-range finish after a well-worked move from Pep Guardiola's side.
Torres netted his seventh goal of the season 10 minutes after half-time after some error-strewn defensive play by Newcastle.
Newcastle's chances at the other end were fleeting as it succumbed to a 12th consecutive Etihad defeat.
City quickly found its rhythm and a slick move saw Joao Cancelo find Raheem Sterling with a superb pass, and he skilfully cut the ball back for Gundogan to fire home.
The goal was Gundogan's second in Premier League this season, which is as many as he got in 31 games last season.
Kevin De Bruyne had Newcastle goalkeeper Karl Darlow scrambling back to palm the ball away moments later when a mis-hit cross into the box looked to be dipping under the crossbar.
De Bruyne broke clear of the Newcastle defence just after the half-hour mark but the alert Darlow rushed off his line to narrow the angle and saved well.
Newcastle rarely threatened at the other end and, despite finishing the first half positively, they still failed to register a single shot on target in the opening 45 minutes.
A Jacob Murphy angled shot just after the break forced Ederson to make his first meaningful save before City added a second.
Newcastle twice failed to clear its lines, with Miguel Almiron and Federico Fernandez both guilty of sloppy play, and the ball dropped for Torres to confidently strike it past Darlow.
The brilliant Darlow denied substitute Sergio Aguero the chance to put the gloss on the result with a fine save from close range late on after another sweeping City attacking move.