The Norwegian, 20, latched on to a superb lofted pass from fellow substitute Kevin de Bruyne and showed superb footwork to take the ball pass Martin Dubravka and tap into the empty net.
It rounded off a brilliant game that saw both sides dominate periods, but City controlled the second half and showed the fight and quality to seal what could be a huge win come the end of the season.
While Bobb enjoyed his first Premier League goal, the success was sparked by De Bruyne.
Just four minutes and 35 seconds after he came off the bench, the Belgian found space in between the home defence and midfield before sweeping a finish into the far corner.
Bernardo Silva had put the Premier League champions ahead in the 26th minute, meeting Kyle Walker’s right-wing cross with an audacious backheel, before two goals in three minutes put Newcastle in charge.
First, Alexander Isak collected a sweeping Bruno Guimaraes pass before curling past City’s reserve keeper Stefan Ortega – who had replaced the injured Ederson – and into the top corner for his fourth goal in four games.
Then, Anthony Gordon was released down the left and he took advantage of Walker backing off to spectacularly curl into the bottom corner and send the home fans into raptures.
City had only lost once in 72 Premier League games when taking the lead and that was under serious threat until their talisman De Bruyne continued his comeback from injury with a top-class strike and a wonderful assist for Bobb.
Boss Pep Guardiola and the entire City squad, including substitutes, celebrated emphatically at the full-time whistle as the reigning champions savoured a third successive league win and sixth in all competitions.
For large parts of this season City have been far from the level that saw them win the Treble last season, especially defensively.
Those issues reared their head again, and will lead to questions about the summer recruitment, with some poor defending for both Newcastle goals.
This was also another game where they missed a host of chances, including Julian Alvarez screwing a golden chance over the bar from eight yards when they were behind.
In De Bruyne though, they have one of the best playmakers in the world or, arguably, the best.
He drifted effortlessly into space for his crucial 74th-minute equaliser and his perfectly-placed low finish was a reminder of his game-changing talent.
The 32-year-old’s last league appearance was in August at Burnley after being sidelined with a hamstring injury.
And De Bruyne still had time to make another big impact in the first minute of added time, one befitting of the game, with his pass behind Kieran Trippier for Bobb simply exquisite.
The forward had drifted in from the left wing and showed superb close control before slotting home to continue his own impressive campaign.
As they edged ominously closer to leaders Liverpool, the Blues will now feel they are in a position to go on one of their famous title-winning runs.
Their next five league games are against bottom-half sides, with four at home and where they were unbeaten in 2023.
It remains to be seen if goalkeeper Ederson will be available for those games after he was forced off in the eighth minute following a collision with City full-back Walker and Sean Longstaff that saw Newcastle have a goal disallowed for offside.
Newcastle show fight but struggles continue
The result will hurt Newcastle, with Eddie Howe’s side now losing seven of their past 10 Premier League games, which is the same as in their 44 games before that run started.
However, there were encouraging signs throughout an enthralling encounter.
Defensively, despite conceding three goals, they were resolute, putting bodies on the line on numerous occasions as City poured forward with attack after attack.
Guimaraes did brilliantly to deny Phil Foden and Rodri in one dangerous attack, while Fabian Schar also blocked an Alvarez effort.
Their goals were fast and incisive and what we have grown accustomed to seeing from their attack under Howe.
Swedish striker Isak was also foiled by Ortega in a one-on-one opportunity shortly before half-time. If converted, that may have put the game beyond City’s reach.
Ultimately, as was the case in defeats at Chelsea in the Carabao Cup quarter-finals and Liverpool in the Premier League at the turn of the year, Howe lacked quality options off the bench to affect the outcome and made one change against City.
It has made life tough for Newcastle this season and, having lost successive home games for the first time under the former Bournemouth boss, they are in 10th place and 11 points off a Champions League spot.
