The 30-year-old faced being punished for swinging an arm towards opposition winger Waisake Naholo during Saturday's second Test, which the Lions won 24-21 to set up a thrilling decider in Auckland.
Irish back row O'Brien denied the offence, however, and the citing has been thrown out by a three-man panel as the incident was deemed to be unintentional.
Williams has since apologised, telling reporters: "They've come to the conclusion that it was reckless - it wasn't intentional. I'm very disappointed that I've let my brothers down."
New Zealand failed to score a try in the second-Test meeting - the first time that has happened in 39 outings.