Pettini and Aadil Ali put on 104 for the second wicket, while Tom Wells hit 67 off 44 balls as Leicestershire reached 363-7 from their 50 overs.
Warwickshire opener Sam Hain made 103 from 107 balls, adding 118 for the fourth wicket with Tim Ambrose (83).
But no other batsman was able to score 30 or more as the visitors were bowled out for 260 in the 44th.
Leicestershire's total was their highest in limited-overs cricket against another first-class county, beating the 344-4 set against Durham in a 45-over competition in 2004.
The Foxes have now won two of their opening three games in the competition, while defending champions Warwickshire have lost twice in their first three games.
Leicestershire all-rounder Tom Wells told BBC Radio Leicester:
"We knew it was a good pitch and that we needed to start well, but Mark Pettini and Cameron Delport complement each other really well up at the top of the order and they gave us momentum.
"Aadil Ali has come into the team and taken his chance, and those three set the platform for us to come in and have a dip at the end.
"The way the game is going these days you never know if you've got a defendable score. People are chasing down scores of 400, but we knew a couple of tight overs could build a bit of pressure, and in the end that told - and Aadil's catch running back to dismiss Sam Hain was brilliant.
Warwickshire coach Jim Troughton told BBC WM:
"In the last couple of games, we've been chasing above-par scores. It hasn't gone well with the ball, and scoreboard pressure has got the better of us.
"It's not for want of the guys putting in the work and trying to nail the skills, but we have to get them right as soon as we can so we give ourselves a better chance with the bat.
"The wicket may have got a little bit tired as the day went on, but they played good shots, came at us hard and, with Pettini scoring a big hundred, guys could play around him. That's how you get to a big total like that."
Mark Pettini hit a career-best 159 from 135 deliveries to help Leicestershire beat Warwickshire in the One-Day Cup.