Left-handed Morgan -- who reached three figures with a six -- came to the crease at 118 for four and added 213 with Paul Collingwood, who was 81 not out at close at Trent Bridge.
Mohammad Aamer had earlier claimed three wickets and was the only bowler to pose a regular threat, finishing the day with three for 39 from 19 overs. Morgan's innings may have cemented his name in the reckoning for the Ashes tour in November and served to illustrate the growing strength of England's middle-order, with the injured Ian Bell to come back.
While Morgan's enterprising 182-ball innings, which comprised 18 fours and one six, was chanceless, Collingwood struggled for fluency but battled through. Morgan was at his best before tea, when he was particularly aggressive against the spinners Kaneria and Shoaib Malik, striking six boundaries in 12 balls at one stage. One such boundary was a reverse sweep to third man off Kaneria, a shot he has become renowned for in one-day cricket.
His 17th four, stroked gracefully through cover off Mohammad Asif, was perhaps his most elegant, and it raised England's 300. Pakistan's players wore black armbands in memory of the 152 passengers who died in a plane crash in Islamabad on Wednesday.