Matthew Wood top-scored with 61 as Notts Outlaws chased down a season-high winning target at Grace Road.
Hodge hit 103 off 66 balls as Leicestershire posted 182-3 but half-centuries from Wood and Ali Brown (55) saw Notts register victory with nine balls to spare.
“Leicestershire’s score was very competitive but we knocked it off quite easily in the end,” said Brown.
“Every total is achievable if you stay positive throughout twenty overs and we did that today.”
Brown shared an opening stand of 47 with Alex Hales who was caught by Josh Cobb off Matthew Hoggard for 29.
“Myself and Alex didn’t want to go too hard too early and without David Hussey in the side we were watchful but positive and only losing one wicket in the first six overs helped us,” said Brown.
“Momentum is key in this competition and early form has stood us in good stead but we must maintain our form.”
Samit Patel (16) and Steven Mullaney (12) took Notts past the post after Wood and Brown were caught out playing positive shots but with the Outlaws always ahead of the required rate, a third successive Friends Provident t20 was always on the cards.