Williams, whose status as world No 1 is under attack from several fronts, delivered a message that she will not be surrendering the top spot without a fight, needing just 63 minutes to dispatch the 29th-ranked Russian.
Germany's Angelique Kerber and Spain's Garbine Muguruza, who have both beaten Williams in slam finals this season, along with Poland's Agnieszka Radwanska, will all be eyeing the No 1 ranking should the American's bid for a 23rd grand slam title stall.
Williams has held the No 1 spot since February 18, 2013 and will extend her streak to 186 consecutive weeks by the end of the US Open fortnight, tying the WTA record currently held by Steffi Graf.
Back on Arthur Ashe Stadium court for the first time since a shock loss to Italy's Roberta Vinci in last year's US Open semifinals, Williams made quick work of Makarova to follow the lead of her sister Venus.
Sixth-seeded Venus had provided the opening act for sister Serena when she outlasted Ukraine's Kateryna Kozlova 6-2 5-7 6-4 before turning over the Arthur Ashe Stadium court to her top-seeded sibling.
