The winger opened the scoring early in the second half, heading in after his brother Iñaki's shot was deflected into his path, before further goals from Robert Navarro and Oihan Sancet completed the rout of Atletico Madrid in what was Terzic's first league win at San Mamés. Williams was not shy in pointing to the German's influence on the turnaround.
"The manager we have is spectacular, and you can see it on the pitch," Williams said. "He's instilled a lot of new things in us that we're picking up perfectly.
"In the second half he really got us into the game with a great team talk in the dressing room. We're very happy with the style of play he wants, and we wanted to show it."
The world champion added that the victory carried extra significance coming off the back of an away win.
"These are three points that taste very good because we're also coming off a win away from home," he said.
Saturday's goal was Williams' first for Athletic Club since the opening weekend of last May, when he scored twice in a win over Alavés — a match that, coincidentally, also saw goals from both Navarro and Sancet, the same pair who found the net alongside him this time.
The winger has now been directly involved in the club's biggest results of the calendar year, having also played a central role in ending Athletic's 40-year wait for a major trophy with last season's Copa del Rey triumph.
Terzic's side have now won back-to-back league matches for the first time under the German, who arrived from Borussia Dortmund in the summer to replace Ernesto Valverde. The head coach has also kept a clean sheet in each of his last two matches in charge, a defensive foundation that has underpinned Athletic's rapid improvement after an underwhelming start to the campaign.
Williams' emergence as a match-winner comes despite growing transfer speculation surrounding the 24-year-old, whose contract at San Mamés runs until 2035 following a bumper renewal agreed after Barcelona's interest in signing him collapsed. For now, at least, his focus appears firmly fixed on Bilbao.