Morrison also helped Canada collect a silver medal in the men's team pursuit.
Morrison's second-place finish gave him the ninth individual medal of his career at the world single distance championships, tying him with Wotherspoon and Groves, who are both retired.
The Fort St. John, B.C., native won his fifth medal in the 1,500-metre event at the worlds, to go along with the two gold and two bronze medals.
Morrison, who won bronze in the 1,500 metres at the 2014 Olympic Games in Sochi, finished Friday's race in one minute 45.08 seconds.
"The race went as planned," said Morrison. "I started attacking in the second lap, and then I just trusted the plan and what my coaches told me, in that I was in good enough shape to hang on until the end. And I did, I hung on quite well in the last lap."
Russia's Denis Yuskov won his second world title in a row in the 1,500 metres, picking up gold in 1:43.36 after also winning the event at the 2013 world single distance championships in Sochi. Dutch skater Koen Verweij, who won silver at the Sochi Olympics, was third in 1:45.15.
In the team pursuit, Morrison teamed up with Calagry's Ted-Jan Bloemen and Jordan Belchos of Markham, Ont. to finish second in 3:44.09. It was their fastest time in the event this season. The Dutch team won gold, for a third straight year, in 3:41.40 and South Korea took bronze in 3:44.96.
"This is the result of work done over months, it didn't happen overnight," said Morrison. "With (Bloemen) coming over this summer, it was a new team, and we struggled early on this season. So we had to communicate, find out what our flaws were, correct our flaws, and we had better results... And today, it all came together. This is just the beginning for us, on the road to the 2018 Olympics."
Bloemen won his first medal with the Canadian team since he moved to his father's country of birth, last summer. He skated for the Netherlands in the past, but these are his first World Single Distance Championships.
"We went out of the gate really fast with Denny, and I was able to maintain my speed pretty well after that," said Bloemen. "And with two laps to go, I gave it my all. It was an awesome feeling."