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Multan, which had won its three previous home games in Lahore, was in all sorts of trouble at 102-6 in 16.5 overs before heavy rain denied further play at Gaddafi Stadium and the umpires called off the game at 10:45 pm local time. Both teams were awarded one point each.
After the Sultans, Islamabad United and Peshawar Zalmi had seven points, and Karachi also had seven points but was fourth overall on net run rate.
Veteran Shahid Afridi hit three sixes and a four in top scoring with an unbeaten 35 off 17 balls as the rest of the Multan top order crumbled against Karachi's pace and spin.
Karachi fast bowler Aamer Yamin, who has played four ODIs and two Twenty20s for Pakistan, got the two key overseas wickets of Moeen Ali (29) and Rilee Rossouw off successive deliveries. Captain Imad Wasim had 2-14.
In a doubleheader on Saturday, Islamabad plays Peshawar at Rawalpindi, while bottom-placed Lahore Qalandars meet Quetta Gladiators at Lahore.