Irfan Wahid, 16, died on February 10 after a suffering a single stab wound on Harehills Lane.
They had fought over a schoolgirl they both had affections for, a jury head.
Detective Superintendent Pat Twiggs of Protective Services Crime, said: "This is a tragic case which has left two families devastated.
"Irfan Wahid had his whole life ahead of him and had it tragically cut short. Another teenager now faces time in prison because of the events that day.
"A simple disagreement over a trivial matter led to Irfan’s death and what we must all now do is ensure his death was not in vain. It is vital the community and in particular young people embrace and remember some simple messages - do not carry knives, do not use them to settle your differences and most importantly do not think that carrying a knife earns you respect.
“Knife crime causes nothing but misery and will earn you a long prison sentence.
"Hopefully Irfan’s family can find some solace in and start to move on with their lives but I know that this has been an incredibly difficult time for them.
"As a force we take knife crime extremely seriously and we want to reduce the amount of these weapons on our streets and to make sure they don't fall into the wrong hands.
"I would therefore appeal to anyone who knows of people carrying knives or other deadly weapons to contact us so we can take action. We need the community to reject the idea that it is OK to carry a knife.
"It could be your son or your daughter either being killed or seriously wounded or starting a long prison sentence because of a minor argument."