Skipper Gautam Gambhir (45 not out) and Manoj Tiwary (34 not out) helped Kolkata win with an unfinished 85-run stand for the third wicket.
Kolkata and Mumbai each have 10 points, followed by Bangalore (nine), Rajasthan (nine), Chennai (eight), Deccan (six), Delhi (six), Punjab (six), Kochi (six) and Pune (four).
Kings XI Punjab 119-6 in 20 overs (D. Karthik 42, A. Gilchrist 26; Iqbal Abdulla 2-19) lost to Kolkata Knight Riders 120-2 in 17.2 overs (G. Gambhir 45 not out, M. Tiwary 34 not out, E. Morgan 28) by eight wickets.
Delhi Daredevils vs Kochi Tuskers Kerala
In another match, Virender Sehwag smashed a 47-ball 80 on a difficult pitch to set up Delhi Daredevils' 38-run win over Kochi Tuskers Kerala on Saturday.
The skipper hit five sixes and eight fours as Delhi posted 157-7 before dismissing Kochi for 119 for their third victory in eight matches of the Twenty20 tournament.
Delhi pacemen earlier did the maximum damage, with South African Morne Morkel emerging the most successful bowler with 3-18 off four overs. Seamers Irfan Pathan and Ajit Agarkar each took two wickets.
South African left-arm spinner Roelof van der Merwe completed the victory when he bagged the last three wickets in one over.
Ravindra Jadeja (31) and Australian Brad Hodge (27) were the main run-getters for Kochi, who suffered their fifth defeat in eight matches.
Delhi were struggling at 35-3 after electing to bat on a slow track where the ball sometimes kept low, but opener Sehwag steadied the innings with a 56-run stand for the fourth wicket with Yogesh Nagar (22).
Sehwag stepped up the run-rate after his team managed just 46 runs in the opening 10 overs, hitting left-arm spinner Jadeja for two successive sixes. He scored 49 runs off the last 15 balls he faced.
The Delhi captain completed his half-century in style, pulling seamer Vinay Kumar over mid-wicket for a six. He fell in the 18th over attempting another big shot, caught in the deep off Kumar.
Sehwag put on 41 for the fifth wicket with Australian Travis Brit, who contributed a 13-ball 20 with the help of one six and two fours.
Fast bowler Shanthakumaran Sreesanth jolted Delhi with two wickets in his opening over as he bowled Australian David Warner and then trapped Naman Ojha lbw with deliveries that kept low.
Delhi Daredevils 157-7 in 20 overs (V. Sehwag 80; Y. Nagar 22, T. Brit 20; S. Sreesanth 2-10) beat Kochi Tuskers Kerala 119 in 18.5 overs (R. Jadeja 31, B. Hodge 27; M. Morkel 3-18, R. van der Merwe 3-20, Irfan Pathan 2-27, A. Agarkar 2-23) by 38 runs.