The Challenge Tour graduate, who could have played professional cricket and roomed with England opener Alastair Cook before choosing golf, added a seven under 65 to his opening 67 for a 12 under 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.
"When I holed the eagle at the first, I said to my caddie ‘It's early but let's just play as well as I can and try not to get ahead of myself'.
"I just kept trying to make birdies and get as far ahead as I could. Anyone who says they don't look at leaderboards is lying - they're in your face. It was nice to keep looking and seeing I was ahead."
At one stage Morrison had stretched his advantage to five shots, but by the close Murray - playing only his seventh European Tour event - had closed that gap to one.
Having been part of a four-way tie for the first round lead with home favourite José Filipe Lima and English pair Chris Gane and Ben Evans, Murray produced seven birdies and two bogeys in a 67.
"I was delighted with that," he said. "I played better than I did yesterday so hopefully I can just keep it going into the weekend.
"I rode my luck on the second and third holes (11th and 12th) but after that I just played nicely and gave myself a chance every hole. I think I hit 16 or 17 greens, so it was good. The wind's changed quite a bit from yesterday so it was a little trickier."
Ireland's Simon Thornton sits third on ten under, but the Qualifying School graduate could be forgiven if he has other things on his mind this weekend - his 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, Scottish duo Jamie McLeary and Andrew McArthur and Spain's Alejandro Cañizares share a distant fourth on seven 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 German Bernd Ritthammer had a hole in one at the seventh, also with a four iron from 220 yards.