This was Mumbai's fourth Hazare title and the one to remember for Shaw (827 runs), who now holds the record for highest runs scored in single edition of the competition.
Samarth and Devdutt Padikkal (101) put on 249 for the first wicket as Karnataka amassed 338/3 in 50 overs. Kerala could only manage 258 in reply.
Sanju, who returned to his home in Thiruvananthapuram after the team's win over Bihar in Elite Group C, has been advised a two-week rest.
Kerala's only loss in the group stage was at the hands of Karnataka.
Kerala rode on the consistent performances of senior players Sachin Baby, pacer S Sreesanth and outstation professionals Robin Uthappa and Jalaj Saxena to progress from a tough group.
Chasing a target of 149, Kerala romped home in just 8.5 overs.
Both Karnataka and Kerala have 12 points from four matches. Kerala take on Bihar in their final Elite Group C match on Sunday.
Prithvi smashed an unbeaten 227 off just 152 balls to help Mumbai post a mammoth 457/4 against Puducherry.
Chasing a daunting target of 352, Railways were bowled out for 344.
This was Kerala's second victory on the trot in Elite Group C.