Officers were called to reports three men had been assaulted in Commercial Street at just before 3.50am.
All three were taken to hospital with stab wounds.
A 21-year-old man was pronounced dead a short time later, while police revealed on Monday a second man, aged 19, died late on Sunday evening.
The third man, aged 18, has been treated for an injury that was not life-threatening.
Three men, two aged 18 and one aged 19, have been arrested in connection with the incident and all remained in police custody on Monday.
Senior Investigating Officer, Detective Chief Inspector Matt Holdsworth, said on Monday: “This is an extremely serious incident which has resulted in the death of two young men and a further man injured.
“We have specialist officers supporting both of their families and are determined to get answers for them and ensure that the person or people responsible are made to face justice for their actions.
“What I would ask for now is the support of the wider public in providing any information about what has taken place or the events leading up to it. I understand that people were present in the area at the time of the incident, and I would urge anyone with information, dash cam or phone footage which could be relevant to our investigation to please make contact.
“I understand people locally will be rightly concerned and I want to reassure people that we are doing everything we can to investigate all possible lines of enquiry to understand the full circumstances of what took place.
“There is still a significant scene in place this morning, with a smaller scene remaining while we conduct forensic enquiries. I would like to thank residents and businesses for their understanding during this time.”
Anyone with information that may assist the investigation is asked to contact the Homicide and Major Enquiry Team via 101 quoting Operation Pochard, reference number 215 of 1st October or online at www.westyorkshire.police.uk/101livechat.