The Premier League's record signing provided a masterclass in creative, incisive attacking play, and Pompey had no answer to his speed of mind and body.
The Brazilian supplied an inch-perfect pass for Jo to open the scoring on 13 minutes before Richard Dunne added a second shortly afterwards.
Robinho then scored with a cool finish on 57 minutes, Shaun Wright-Phillips added a fourth, substitute Ched Evans made it five finishing off a remarkable goal, and Gelson Fernandes completed the rout.
Despite the mammoth £32.5 million fee paid to bring Robinho to Eastlands, some doubted whether the quicksilver forward could really succeed in the fast, physical Premier League.
The early signs suggest Robinho's impact will be spectacular.
Last weekend against Chelsea he scored a free-kick and dictated play for City, but a wonky radar meant he surrendered possession as often as he found a team-mate.
This time he added precision to his dizzying array of skills, spraying visionary passes and beating defenders with almost embarrassing ease.
As early as the third minute, he had David James at full stretch with a pinpoint shot, but shortly afterwards he turned provider, laying on a superb diagonal through ball for Jo, who rounded James and finished left-footed.
The pair combined with intuitive brilliance, allowing Jo to start showing why City paid £18m for his services.
City soon extended their lead following a 20th-minute Elano corner. James patted the ball weakly away and captain Dunne pounced to bundle the ball home.
Portsmouth manager Harry Redknapp quickly brought Papa Bouba Diop and John Utaka off the bench but, if anything, they made things worse.
Robinho himself made it three just before the hour. Stephen Ireland drilled a diagonal ball that Jo brought down and laid off to the former Real Madrid man, who slotted home from the edge of the box.
Cue a samba dancing celebration in which Ireland attempted, unsuccessfully, to match the moves of Brazilian trio Robinho, Jo and Elano.
Robinho has now scored in both Premier League games and, even more importantly, created a buzz of dizzying excitement around the blue half of Manchester.
As with City legend Georgi Kinkladze, every time Robinho gets on the ball there is a very real possibility of something extraordinary happening.
Portsmouth were in tatters, and Wright-Phillips took full advantage, running onto another excellent Ireland through-ball and smashing past James at his near post.
More humiliation was to come after 78 minutes. Robinho bamboozled his man on the left side before crossing low for Wright-Phillips. He backheeled brilliantly into the path of Evans whose finish was low and true. Sensational.
Another James howler allowed Gelson to score the final goal. The keeper failed to deal with a low Javier Garrido cross and cleared only to the edge of the box, where Gelson reacted quickest to finish off a devastating performance.
City's new owners have made much of their ambition to qualify for the Champions League this season. After this demolition job, a top-four finish does not seem so far-fetched.
