The Australian gave the team their first top five finish after Reinardt Janse van Rensburg finished sixth in the opening stage.
Morton followed Ian Boswell (Team Sky) seven seconds behind top two Rafal Majka (Bora-Hansgrohe) and George Bennett (Team LottoNl-Jumbo).
The team had Scott Thwaites in the initial lead group that formed after roughly 40km and the British rider was instrumental in placing Morton in the final lead group.
Thwaites continued to follow as Tom Skuijins (Cannondale-Drapac) and Daniel Jaramillo (United Healthcare) led what was left of the break over the hors categorie Mount Hamilton.
On the descent Thwaites led Morton and opened a gap to what was left of the peloton.
Together the Dimension Data pair and the rest of the chasers caught the riders up the road and formed a lead group of seven.
Quimby Road was the undoing of many as the lead group disintegrated and while Morton continued to push on with a new lead group, Thwaites fell behind.
“I’m pleased with how today went and I felt pretty good,” said Morton.
“It took a while for the break to go and we were lucky to have Scott in there for us.
“We were lucky to catch Scott at the top (of Mount Hamilton) and then we hit that descent pretty hard.
“We rode well all the way until the final kilometre really and I was always feeling pretty good.
“In the end, us four just raced each other over that final kilometre but I can be happy with how the legs were,” he said.
Morton will start the 192km third stage in the young rider’s jersey.