An officer with British Transport Police said that his "instincts took over" when he heard screams coming from a rail platform.
Sergeant Lee Valentine told BBC News that he had no idea what he was running into as he responded to the sounds of distress with other officers hot on his heels.
"When we saw the man wielding a knife, instinct took over and we were able to... successfully detain the male," Valentine said.
Chief Constable Paul Crowther said, "I think they were heroes - they don't think that themselves. They were really concerned for the other people who were injured and for the Metrolink staff."
He added: "Their quick-thinking and outstanding response helped to prevent more passengers being hurt and stands as a testament to the force."
Sergeant Valentine was wounded in the incident, suffering several lacerations. He was transported to a nearby hospital where he was treated and released.
No details have been released on the status of the victims of the knife assault.