Morgan is impressive on debut for Ospreys.
The Falcons were 13-0 up on the half hour, but four penalties from debutant Matthew Morgan and an opportunist try from Gareth Owen dragged the Ospreys back into the match in the second half after Luke Fielden had grabbed his second try of the game.
At 18-17, the Ospreys had a real chance to snatch victory when Owen hit the bar with a long-range penalty. But Newcastle survived and could have scored a third try in the dying minutes of the match.
Falcons coach Alan Tait felt his side deserved the win, but admitted he thought his young team were on the point of throwing the match away in the closing quarter of the game.
"Key decisions in key areas nearly cost us the game," said Tait.
"Their try was unnecessary and I ended up with a few more grey hairs as they chipped away and I did think we were going to throw it away.
"All credit to Ospreys. They brought a young side and they chipped away and they had a real exciting kid in Matthew Morgan. We failed to get a line on him and stop him.
"We did some silly things and we will sit down and have a look at what we did in that last quarter.
"We don't tell the players when to kick and when to run, but to play on what is there in front of them.
"I thought we did really well in the forwards, especially our front row, who were up against Duncan Jones and Mefin Davies, who are top-class performers.
"We've talked and listened to referees who have told us they will favour the dominant side in the scrum, but that just didn't happen tonight.
"We're off to a winning start in this competition, but we have Harlequins away next week and that will be tough as we are struggling in the second row with injuries to Filipo Levi and Glen Townson."