But Levi made his 64 balls count, hitting five sixes in his 80 to knock the top off the 264-run target and afford his teammates more time to come to grips with conditions even as wickets fell in the middle overs.
By the time Levi pulled a short ball from Jean Symes straight to the fielder at deep midwicket, the Cobras had 109 on the board and the equation had been reduced to 155 runs needed from 186 balls.
Puttick held the middle part of the innings together until a Matt McGillivray delivery kept low to trap him lbw for 56 - a score that took his tally in the competition to 450 runs from six innings at an average of 90.
Although that sparked a small wobble, Yaseen Vallie (39 not out) and Sybrand Engelbrecht (47 not out) showed composure and style to put on an unbroken 83 and see the Cobras home with 11 balls to spare.
While all but one of the Lions batsmen reached double figures after they were stuck in to bat by Cobras skipper Robin Peterson, Goolam Bodi’s 54 was the highest score and so the hosts were only able to manage 263 for eight, which proved about 20 runs short.
The Lions were not helped by their running, with Bodi and Dominic Hendricks (38) dismissed when mix-ups were seized on by some sharp fielding from Dane Paterson and Rory Kleinveldt.
The Cobras experience with the ball was also telling, with Kleinveldt and Justin Kemp taking a combined 3 for 69 in their 20 overs.
Victory put the Cobras on 25 points after seven games, while the Lions were left in third place on 15 points and will have the fourth-placed Titans breathing down their neck next week.
Michael Owen Smith