Left-hander 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 the 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.
It also helped justify Andrew Strauss's decision to bat after winning the toss in overcast weather that eventually gave way to sunshine.
Pakistan, seeking to avenge their 3-0 series loss in England in 2006, started well with four early wickets but glaring errors by wicketkeeper Kamran Akmal as well as some wayward bowling meant they could not capitalise.
Pakistan also suffered from the Decision Review System (DRS), which was employed in England for the first time.
The tourists incorrectly challenged two umpiring decisions to lose their two allocated reviews while England had two successful reviews and lost one.
While Morgan's enterprising 182-ball innings, which comprised 18 fours and one six, was chanceless, Collingwood struggled for fluency but battled through.
He survived one chance when he should have been stumped on 48 when beaten by a ripping leg-break from Danish Kaneria, but keeper Akmal fumbled the ball.
Akmal, who struggled with his glovework on the 2006 tour of England and also dropped several chances in Australia in December-January, dropped a simple chance off Strauss when the England opener had scored 15. Strauss went on to make 45.
RUSTY PIETERSEN
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. Former Ireland player Morgan is playing in just his third Test.
Earlier, Aamer claimed three of the first four wickets by having Alastair Cook (8) caught at first slip and Strauss caught behind to a short and wide ball.
After Asif bowled a rusty-looking Kevin Pietersen for nine off the inside edge, Aamer trapped Jonathan Trott lbw having played no shot. Trott unsuccessfully challenged his dismissal.
Pakistan's two referrals were lost in the space of two Asif overs after Pietersen was given not out by Sri Lanka umpire Asoka de Silva, first lbw and then caught behind.
The luckless Kaneria struggled with his control but, added to his missed stumping, had two wickets overturned. Trott (on 13) and Morgan (on 78) were given lbw but England challenged both legitimately.
Morgan and Collingwood beat England's previous best fifth-wicket stand against Pakistan of 192 between Denis Compton and Trevor Bailey, also at Trent Bridge.
The dry pitch is turning and showing early signs of uneven bounce.
Pakistan's players wore black armbands in memory of the 152 passengers who died in a plane crash in the hills north of Islamabad on Wednesday.