Australia captain Pat Cummins (30) briefly held that honour after Sunrisers Hyderabad agreed to splash $2.46 million for his service before Starc bettered that mark.
Barely a month after leading Australia to the 50-overs World Cup title in India, Cummins entered the auction with a base price of 20 million Indian rupees ($240,473).
IPL heavyweights Mumbai Indians and Chennai Super Kings were initially interested in him but both dropped out as a two-way bidding war ensued.
Royal Challengers Bangalore doggedly pursued Cummins but 2016 champions Hyderabad had the last laugh in the tug-of-war over the fast bowler, who has also evolved as a handy lower-order hitter.
England all-rounder Sam Curran's 185 million rupees bid from Punjab Kings at last year's auction was the previous highest mark.
Cummins also provides a leadership option at Hyderabad, though head coach Daniel Vettori remain tight-lipped about that prospect.
"There's a lot of cricket left before the IPL," former New Zealand captain Vettori said.
"We'll have to get through that and then we'll make a decision closer to that time."
Back after an eight-year gap, left-arm quick Starc was in demand as soon as his name was put under the hammer with Mumbai and Delhi vying for his service.
Both, however, retreated as bidding intensified and Kolkata trumped Gujarat Titans by offering the winning bid for the quick.
"You should expect this. Because IPL is growing, salary caps will grow and so will player fees," Kolkata chief executive Venky Mysore said of their aggressive pursuit of Starc.
New Zealand's Daryl Mitchell (32) also struck it rich after Chennai splashed 140 million rupees to acquire the batting all-rounder at 10 times his base price.
India seamer Harshal Patel (33) also became a millionaire joining Punjab Kings for 117.5 million rupees in the auction, which was held outside India for the first time.
The Indian cricket board has not announced the dates but next year's IPL is likely to be played between March and May.
Unsold players included former Australia captain Steve Smith and England spinner Adil Rashid.
