Rhys Jones, who was 36 and originally from Blackwood, died from his injuries at the Royal Gwent Hospital after the incident in Clarence Place on 24 November.
Rhys Barnes, 28, of no fixed abode, admitted his murder at Cardiff Crown Court on Monday.
He was remanded in custody and will be sentenced on 24 March.
A man has admitted murdering another man during a stabbing at a homeless shelter in Newport.