The victory means that Leith hold onto their second-placed position, five points behind Dalkeith CYP. Young Stars sit in mid-table.
Two early goals for Leith made the difference with set-piece specialist Ryan Cunningham integral to the victory.
Young Stars will feel that the scoreline should perhaps have been closer.
Cunningham proved his worth within the first two minutes, when his corner from the right met the head of Kyle Jimenez, who directed the ball into the right corner of the goal.
Just a minute later Cunningham’s free-kick from 30 yards sailed into the roof of the net to double the lead.
Young Stars pulled a goal back after 18 minutes when Seth Allen played a perfect pass down the left wing into the path of Craig Urquhart. He cut in from the left before finishing low past Leith goalkeeper Scott Aris.
Cunningham grabbed his second goal, and Leith’s third, after 26 minutes, shooting into the bottom left corner from ten yards.
Young Stars should have pulled a goal back moments before half-time when Ronan Gorrian did all the hard work by dribbling round Aris, however Liam Cubitt managed to sprint back to the line to clear the ball when it looked destined for the net. Leith extended their lead further after 50 minutes when Robbie Howie’s crossfield ball evaded the Young Stars defence and trialist Arran Connery shot into the net from the right side of the six-yard box.
And they had a goal disallowed two minutes later when Howie headed the ball into the top left corner, but he was deemed to be offside.
Young Stars pulled a goal back with their next attack as Jamie Hamilton’s shot beat Aris from 12 yards.
Goalkeeper Matthew Morris pulled off a marvellous low save when Leith’s Alexander Calder-Crease shot powerfully from the edge of the penalty area.
Leith completed the scoring in the final few minutes as Howie dribbled clear of the Young Stars defence before powering the ball into the net.
Iain Aris, Leith coach, said: “It was a good match played in a strong wind and that made for an exciting game. I think we were the stronger team and we deserved to edge it.
“We’ve got a lot of strong players and we can hopefully secure promotion this season.
“Being the third best Leith Athletic team at this age group, we usually don’t get as much attention as the other teams and the guys are really enjoying being competitive and they’re all enjoying their football.”
Young Stars coach, Paul Cameron, said: “We gave ourselves a mountain to climb after giving away two goals in the first five minutes. The first goal was down to a defensive mistake as we didn’t play our lines correctly.
“We couldn’t do much about the second goal.
“It was a really good free-kick high into the net. We had a couple of clear cut chances in the first half which we really should have taken to get us back into the game by half-time. In the second half, things just didn’t fall for us.
“I don’t think we were outplayed. At the end of the day, we weren’t quite as physical as we wanted to be and we didn’t take the chances that came our way.”
Musselburgh Young Stars: Matthew Morris, Ross McGuire, Jason Cameron, Jack Tucker, Matthew Cameron, Craig Urquhart, Euan Fraser, Seth Allen, Scott Broughton, Ronan Garrion, Connor Conroy, Callum Skinner, Brandon Gilfillan, Liam Henderson, Shane Pender.
Leith Athletic Whites: Scott Aris, Bradley Spinks, Ryan McDougall, Kyle Jimenez, Saran Robertson, Liam Cubitt, Alexander Calder-Crease, Robbie Howie, Aaran Connery, Allan Paterson, Ryan Cunningham, Brandon Hunter, Dillon Laing, Jamie Hamilton, Liam Ashworth, Sean Walker.