Kohli anchored the 147-run chase with authority alongside captain Rajat Patidar as Bengaluru sealed victory in front of a packed M. Chinnaswamy Stadium in only 15.1 overs.
Put in to bat, Lucknow struggled on the batting-friendly surface, crawling to 35-1 in the powerplay before being bundled out for 146.
Defending champions Bengaluru never looked troubled as the 37-year-old Kohli made a fluent 49, including six fours and a six.
Kohli led Bengaluru to 60-1 in the powerplay before Patidar punished the Lucknow attack to add 27 runs with a lively 23-run cameo from Jitesh Sharma, helping complete the chase.
Bengaluru moved level at the top of the standings with Rajasthan Royals on eight points, edging ahead on net run-rate.
Kohli did not field after Bengaluru decided to introduce him as an impact player due to injury.
"I'm still not 100%. My knee was a bit sore last game. I've been under the weather for four or five days now," said Kohli, the leading IPL run-scorer this season.
"I was happy with my intensity. I would have liked to carry on and finish the game off."
Bengaluru's winning foundation had been laid by Dar, who compiled figures of 4-24, well supported by Australian Josh Hazlewood, Bhuvneshwar Kumar and spinner Krunal Pandya.
Lucknow captain Rishabh Pant was forced to retire hurt after being struck on the elbow by a rising delivery from Hazlewood, leaving the field in visible discomfort.
Australian Mitchell Marsh offered resistance but was bowled for 40 by Krunal Pandya before Ayush Badoni (38) and Mukul Choudhary (39) provided late impetus.
Bengaluru host Delhi Capitals on Saturday, and seventh-placed Lucknow face Punjab Kings on Sunday.