Kohli put on 69 with Shubman Gill (46) while a 114-run union with Shreyas Iyer (56) broke the back of the chase for India, who won their tournament opener by beating Bangladesh on Thursday.
Saud Shakeel (62) and Mohammad Rizwan (46) put on 104 for the third wicket but Pakistan badly lost their way from 151 for two in the 34th over, losing their last eight wickets for just 90 runs.
While Iyer and Hardik Pandya departed within successive overs, the only lingering doubt was whether Kohli, who leapfrogged Tendulkar's record for the most ODI tons in 2023, would get to three figures.
Kuldeep Yadav took three for 40 and Kohli claimed a couple of catches to move on to 158, the most by an India outfielder, leapfrogging Mohammad Azharuddin, the previous record holder with 156.
Virat Kohli's record-extending 51st one-day century left India on the verge of the Champions Trophy semi-finals and Pakistan on the brink of elimination.
