Without really looking convincing they scored three, hit the woodwork twice yet almost allowed their Dutch visitors back into the game with indifferent defending.
Manchester City came into the game on the back of two successive Premier League defeats but had the perfect start with a goal after only two minutes.
Shaun Wright Phillips and Jo combined well on the edge of the area freeing the former Chelsea player to fire home.
At this stage City were coasting, moving the ball around well and looking the likeliest to score, yet all this new found confidence disappeared on 16 minutes when Twente scored an unexpected equaliser.
City's defence hesitated as if waiting for the referee to blow for an infringement and Eljero Elia took full advantage bursting clear to shoot past Joe Hart.
The game was now turned on its head as the Dutch side began to control proceedings and the home support grew frustrated at the number of misplaced passes and shaky defending.
Twente looked comfortable without really threatening a second goal and it was only in the final minutes of the half that City looked like taking the lead.
Jo turned his marker beautifully but Sander Boschker was quickly off his line to smother the Brazilians shot. Moments later it was Jo again whose cheeky back heel was comfortably saved.
City showed more urgency in the second half and Jo just failed to get on the end of a Robinho through ball.
Wright Phillps ran at a retreating Twente defence before firing narrowly wide.
The Dutch manager is the much maligned former England coach Steve McClaren who was getting some less than good natured banter from the home support,
Worse was yet to come for the ex-Middlesbrough boss as Robinho restored City's lead on 57 minutes with a glorious curling shot from just inside the penalty area.
Incredibly it was soon three for the home side - Substitute Benjani had only been on the field 4 minutes when his deflected shot found the back of the net.
Twente had already chalked up three points in Group A having started their round of matches earlier and sensed they might get back into this game.
City's defence was enduring some anxious moments as their Dutch visitors created a series of half chances.
Robinho almost settles City's nerves with a driving run and shot which rebounds off the foot of the post. Boschker then made a flying save from Benjani's fierce shot,
Manchester boss Mark Hughes was pleased with the win but acknowledged his teams attacking style can leave them vulnerable at the back.
"We're pleased with the result as it was important we got back on track.
"Robinho could have had a hat trick and his strike for the second goal was fantastic.
"At 3-1 up we were quite comfortable but we just switched off and allowed them a lifeline but fair play to them they played well and made us work hard to close them down.
"We increased the tempo in the second half and were better for it as we played higher up the field.
Hughes also admitted to defensive frailties.
"We know we are vulnerable to the counter attack and need to be better at one v one situations but we don't have many options in defence so on occasions we can be exposed. But we shouldn't be criticised for being attack minded.
"We need to get into the mentality to see games out more comfortably.
"We've got a positive result and that's what you have to do in this competition in your home games."