The club's record buy proved he is a class act by curling a shot from just inside the penalty area over goalkeeper Sander Boschker in the 56th minute.
It was his seventh goal of the season and gave City the advantage after a sublime pass from Stephen Ireland.
Robinho also hit the post twice but City had their work cut out against feisty Dutch opponents, managed by former England boss Steve McClaren.
Shaun Wright-Phillips and Benjani Mwaruwari were also on target but Twente responded with goals from Eljero Elia and Robbie Wielaert.
City got off to a flying start with Wright-Phillips making the breakthrough in the second minute.
He fired a right-foot shot into the corner after a neat one-two with Jo for his fifth goal of the season.
City almost added a second three minutes later but Boschker did just enough to parry Robinho's effort.
The Dutch side, however, drew level in the 17th minute when Elia won the ball, almost booting Pablo Zabaleta in the face in the process.
Referee Nikolay Ivanov allowed play to continue, which caught City cold as they were clearly anticipating a free-kick.
Elia took advantage and showed a quick turn of pace before rifling a shot beyond Joe Hart.
Jo got away from his marker in the 41st minute but his effort showed a lack of confidence and Boschker made a comfortable save.
Then the Brazilian saw his back-heel saved by the goalkeeper in stoppage time after good work by Wright-Phillips.
City got into their stride at the beginning of the second half and Robinho released Jo in the 49th minute but Brazilian defender Douglas did enough to put him off and enable Boschker to tidy up.
Wright-Phillips went close four minutes later as City kept up the pressure, his effort from 20 yards hitting the stanchion at the back of the side-netting.
City regained the lead in the 56th minute with that
spectacular strike from record signing Robinho.
Manager Mark Hughes made a switch in attack in the 59th minute when Benjani, who had recovered from a thigh injury, replaced the ineffective Jo.
The move paid dividends as two minutes later City went 3-1 ahead with Benjani's effort taking a deflection off Douglas to leave the goalkeeper wrong-footed.
Twente, however, refused to lie down and pulled a goal back in the 64th minute thanks to a header from Wielaert.
It was a warning shot to City that this match was far from over.
Twente substitute Stein Huysegems should have pulled them level in the 71st minute but scuffed his shot wide from close range.
That acted as a wake-up call to City with Robinho seeing his effort come back off the inside of the post four minutes later.
Then Boschker did well to parry Benjani's effort in the 77th minute and Robinho saw another shot come back off the post.
Huysegems squandered another great chance of securing a point on the stroke of full-time, failing to find the target from four yards out.
It was a nail-biting finish but City just about deserved it on the balance of play and it was just the result Hughes was looking for following Premier League defeats at the hands of Bolton and Middlesbrough.
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