Zulfiqar Babar, Shoaib Malik and Sunil Narine were the three bowlers to lose their record, having all conceded three runs in a four-over spell.
Morris’ bowling helped keep the Cobras to a score of 94 for nine in response to the Lions’ 141 for seven, giving the Lions a three-point lead over the second-placed Knights at the top of the RAM SLAM T20 table with a game in hand.
The Lions knew they required a disciplined bowling performance after putting up a par score on a slowish Wanderers track on which they had largely struggled with the bat.
With Chris Gayle forced out the game with a back problem, Rassie van der Dussen came in for his first game of the competition and hit 52 from 40 deliveries.
However, the other batsmen failed to get going as four Cobras bowlers conceded less than seven runs per over, with Mthokozisi Shezi making up for a couple of dropped catches with figures of 2 for 23 in four overs.
Richard Levi (20) made a confident start to the Cobras reply, but found himself outwitted by Morris in what turned out to be one of the key moments of the game.
As well as that wicket, Morris’ initial two-over spell cost him absolutely nothing, and fellow seamers Hardus Viljoen and Dwaine Pretorius were also superb, taking a combined 4 for 36 in eight overs as the Cobras crumbled.
The Lions needed to restrict their opponents to 112 or less to grab the bonus point, which they easily managed thanks to Morris’ sensational economy.