After Norwich goalkeeper Aston Oxborough made two fine saves and Cherries goalkeeper Mark Travers denied Louis McIntosh and Tristan Abrahams, Cantwell ran at the Cherries defence and found the net from outside the penalty area to clinch victory.
The result leaves the Canaries four points clear of third-placed AFC Bournemouth, who have a match in hand. Bury are bottom without any points.
Norwich: 26 Jan v Blackburn (A) PL2
AFC Bournemouth: 6 Feb v Bury (H) PL Cup