The Lions also registered three half-centuries but none were as devastating, as they finished up on 284 for seven.
The visitors were somewhat complicit in the Cobras’ heavy scoring, offering Puttick no fewer than six lives during his 111-ball innings.
Puttick put on 101 for the first wicket with Omphile Ramela, who made 40, and then 82 with Van Zyl.
However it was the final partnership that really did for the Lions, as Van Zyl and Ontong added 154 from 75 balls before Ontong was out to the last ball of the innings.
As a result the Cobras set a new ground record as they surpassed the 316 for seven that they scored against the Titans two seasons ago.
Although the Lions made an aggressive start to their reply, with openers, Stephen Cook (58) and Alviro Petersen (49), putting on 97 in the first 15 overs, the middle order was undone by spinners Sybrand Engelbrecht and Robin Peterson.
Peterson took 2 for 30 and Engelbrecht 2 for 55 as the Lions fell from 97 without loss to 138 for five, and only a century stand for the seventh wicket between Dwaine Pretorius and Hardus Viljoen denied the Cobras another bonus point.
The pair never threatened to overhaul the target, but did an excellent job of damage limitation as Pretorius finished unbeaten on 77 and Viljoen got out to the penultimate ball of the game, having just recorded his second List A fifty.
The result means that the Cobras are top of the table with 14 points from three games, while the Dolphins and Lions are both four points back having played an extra game.