Williams moved into the last eight with a 6-1 6-2 victory over Ukrainian qualifier Savchuk in 48 minutes.
Savchuk got off to a flying start in Quebec City, breaking seven-time major winner Williams in the first game of their second-round clash.
But Williams' response was emphatic - winning the first nine points on Savchuk's serve - and breaking all three times to take the first set.
Another two breaks to start the second set saw the American veteran race to a 4-0 lead, dropping just four points in doing so, before Savchuk got on the board with a love hold.
Williams lost serve in the sixth game, but Savchuk could not build on that momentum - getting broken back straight away before the American progressed on her second match point.
Williams will face Czech Lucie Hradecka in the quarter-finals, after Hradecka came from a set and a break down to beat countrywoman and qualifier Barbora Krejcikova 3-6 7-5 6-2.
The world number 22's pathway to the title in Canada was made even easier on Thursday, with second seed Ajla Tomljanovic and eighth seed Timea Babos defeated.
Croatian representative Tomljanovic was no match for Czech Andrea Hlavackova 6-3 3-6 6-3 in a two-hour battle.
Hlavackova will take on fifth-seeded German Julia Goerges for a spot in the semi-finals.
Hungary's Babos was ousted by in-form Croatian Mirjana Lucic-Baroni 7-6 (7-3) 6-2.
Lucic-Baroni snapped an eight-match losing streak with a run to the fourth round of the US Open as a qualifier, and has backed up that run by moving into the last eight.
The 32-year-old faces Kazakhstan's Sesil Karatantcheva in the quarters.