Quincy Amarikwa opened the scoring for Toronto in the 58th minute before Morgan tapped a shot past Quillan Roberts from a yard out after the Toronto keeper fended off a Raheem Sterling strike.
Amarikwa, making his first appearance for Toronto, connected on a rebound past Liverpool keeper Peter Gulacsi for a Toronto team that continued its resurgence under Paul Mariner.
"It was a brilliant day out. I think both teams got what they needed out of the game," Toronto FC midfielder Terry Dunfield said. "I think both teams in each half gave a good account of themselves. There's no hiding that our schedule has been brutal of late."
Liverpool was without many of its stars— including captain Steven Gerrard and England teammates Andy Carroll and Glen Johnson who are rested after the Euro tournament — as it begins its preseason North American tour under new manager Brendan Rodgers.
"You've got to temper your thoughts with where Liverpool are at, the squad that they brought over, but all you can do is your best and I thought we did well under the circumstances," Mariner said.
"Let's not get carried away. If Liverpool brings their first squad and they're further on in their preseason or the season, they're a top-class team with top-class players."
Liverpool fans chanted and sang songs familiar to the terraces at Anfield, including a stirring rendition of the club's anthem "You'll Never Walk Alone."
Supporters of the 18-time English league winners unfurled numerous banners, including one honoring the Hillsborough disaster in which 96 fans were crushed to death in 1989.
Liverpool continues its preseason schedule on Wednesday at Boston's Fenway Park against Italy's A.S. Roma before taking on English rivals Tottenham on July 28 in Baltimore.