The English Challenge Tour graduate, who roomed with England cricketer Alastair Cook before choosing golf as a career, added a 65 to his opening 67 for a 12 under par halfway total.
He eagled the tenth - his first - at Porto Santo Golfe, then birdied five of his next seven to be seven under for the round after just eight holes.
"It was a good day. The first hole I drove a three iron to about 25 feet and rolled it in for an eagle so that was a nice start to the morning," he said.
"Then the next hole I hit it to about four feet and rolled that in, then the 12th I hit a really good putt for birdie that lipped out, so it was a good start. Every hole seemed like I was hitting it on the green and rolling it in - it wasn't like I was holing monster putts.
"I made double bogey on the fourth when I hit it in the water but I recovered well from that. I felt very much in control. I didn't feel like I was getting ahead of myself. It was a very good day."
At one stage Morrison had stretched his advantage to five shots, but Ireland's Simon Thornton closed the gap to two with a round of 66.
But the Qualifying School graduate could be forgiven if he has other things on his mind this weekend - Thornton's wife is due to give birth to their first child on Saturday.
"I won't leave, no," said Thornton about the prospect of flying home if his wife goes into labour. "We made that decision before I came here. It's been nice spending the last few weeks together and now we're approaching D-Day as such.
"That'll be great as well. There was a lot of debate over whether I'd come this week but because of the lack of opportunities in the last month I had to come and play it. If I'd not come here and taken a couple of weeks off then all of a sudden you get a card but not taking the opportunities, I had to come. I keep checking my phone all the time. There's no word yet."
England's John Parry and Spain's Alejandro Cañizares share a distant third on seven under, while out on the course the four overnight leaders were all teeing off in the afternoon.
Scotland's George Murray, home favourite José Filipe Lima and English duo Chris Gane and Ben Evans were all starting their second rounds on six under.
There were some spectacular shots as well as rounds - Scotland's Callum MacAuley, playing with Morrison, holed his four iron tee shot at the 212 yard ninth.
And Bernd Ritthammer had a hole in one at the seventh, also with a four iron from 220 yards. But while MacAuley was safely though on four under, German Ritthammer had a nervous wait to see if he would make the cut.
He finished one under in a tie for 61st and had one shot to spare as the afternoon starters got underway.