No Williams had Renault engines back then and as Renault didnt have a team and Williams and Renault where trying to build a partnership for the future - which eventually collapses when Williams didnt want to become 'Renault'. You'd have to go as far back as 1994 and Schumacher in a Benetton Ford for the last time a customer-engined car won the title, but even then one could argue Ford where investing quite substantially at the time.
In 84 Lauder, then '85-86 Prost won back to back titles in a McLaren TAG - but TAG is 40% owned by Daimler Crysler.
In 82 Rosberg won in a Williams Ford - at a time when Ford where a fairly generic 'customer' engine available to a lot of teams.
In 66-67 Brabham and Hulme respectively where powered to victory in Brabhams with engines by Repco, an engine tuning company, and before that Jim Clark had something of a Climax (boom boom).
Mostly however, other than the Ford era with their widely used 'customer' engines most championships have been won with the backing of a major car manufacturer.