The left-hander's score came from just 65 deliveries as Zimbabwe reached their target of 224 with 28 balls remaining in Bulawayo.
Earlier, Afghanistan, playing in their first ever bilateral ODI series against a Test-playing nation, had reached 223-9 from their 50 overs, with Tendai Chatara (2-37) and Donald Tiripano (2-50) doing their part to restrict the tourists' progress.
They made a poor start when Usman Ghani (0) was tempted by Tiripano's delivery and only succeeded in finding the safe hands of Elton Chigumbura in the second over.
Asghar Stanikzai (8) and Hashmatullah Shaidi (15) failed to stick around and when opener Noor Ali Zadran was run out by wicketkeeper Regis Chakabva for 43, Afghanistan were struggling on 99-4.
However, Samiullah Shenwari (65 not out) and Mohammad Nabi (54) rescued the situation somewhat, the latter's knock coming from just 32 deliveries before Prosper Utseya (1-33) accounted for his dismissal.
Shenwari put on 45 with Shafiqullah (24) for the sixth wicket, but as the latter was accounted for by Tinashe Panyangara (1-41) and the tail failed to provide a telling contribution, Afghanistan reached 223-9 from their 50 overs.
Zimbabwe made an inauspicious start when Vusi Sibanda edged Shapoor Zadran (1-32) to wicketkeeper Shafiqullah for four and Hamilton Masakadza could only add 10.
However, Sikandar Raza (42 not out) and Brendan Taylor (43) picked up the pace and the duo combined for a third-wicket stand of 93 to put the hosts in control.
Taylor was trapped lbw by Shenwari (1-42), but that brought Williams to the crease and he smashed eight fours and a six in his entertaining knock.
He was eventually caught and bowled by Nabi (1-40) but the damage had already been done, as Raza and Chigumbura (39 not out) guided Zimbabwe over the line.
The four-match series continues on Sunday, again in Bulawayo.