New Zealand defeated Pakistan by 79 runs on Wednesday, to win the second One-Day International (ODI) and level the three-match series 1-1.
Conway hit 13 boundaries and a six off 92 balls, his second hundred in one-day internationals.
His stand with Williamson is a record against Pakistan, beating the 159 set in Wellington by Williamson and Martin Guptill in 2016.
Opting to bat first, New Zealand posted a target of 261 runs before bowling out Pakistan for 182 runs in 43 overs, with skipper Tim Southee and Ish Sodhi claiming two wickets, while every other Kiwi bowler took a scalp each.
Spinner Mohammad Nawaz took four wickets to help Pakistan restrict New Zealand to 261 all out on Wednesday after opener Devon Conway hit a century in the second day-night international in Karachi.
Nawaz finished with 4-38 as New Zealand slumped from a strong 183 for one in 29.5 overs to 206-6, losing five wickets for 23 runs in the space of 40 deliveries.