The 18-year-old, who signed for Liverpool from Bayer Leverkusen last week, was inspired during the 3-1 friendly win.
He found the net after two minutes of each half, and set up the final goal for teammate Sebastian Kerk, before getting a standing ovation as he was subbed in the 81st minute.
Sterling lasted 65 minutes, while Morgan was withdrawn with a quarter of an hour remaining.
Meanwhile, Jonjo Shelvey was also on top form as England U-21s prevailed 2-0 in Azerbaijan.
It was his free-kick that set up a glancing header for Steven Caulker to make it 1-0, and the midfielder put the seal on the victory with a well-taken volley late on.
The U-21s were skippered by Jordan Henderson for the Euro 2013 qualifier, while Martin Kelly also started.
Thumbnail photo via Liverpoolfc.com