Swiatek had lost to the 25-year-old Estonian in both of their previous meetings and there were signs of tentativeness during the opening exchanges from the Pole.
Kontaveit took early control of the encounter on centre court to lead 2-0 and she was in command until midway through the set when she failed to extend her lead to 5-3.
From 4-4 both players held their serve to force the tiebreak which Swiatek dominated seven points to four.
Change
The second set was a different tale. Swiatek claimed her opponent’s opening service game and, after saving a break point, held to lead 2-0.
She then just wore Kontaveit down with her speed around the court and penetrating ground strokes.
The 57-minute first set dogfight appeared ancient history. A second set rout lasted 25 merciless minutes during which Kontaveit failed to win a game.
“I’m glad I got my first win against her,” said Swiatek after the 7-6, 6-0 victory.
“She was playing really fast at the start and I began too slowly. But I got back and I’m happy to be playing consistently.”
Defence
The 20-year-old will continue the defence of her crown on Monday against 18-year-old Marta Kostyuk.
The Ukrainian, who accounted for the 2016 champion Garbine Muguruza in the first round, disposed of Varvara Gracheva 6-1, 6-2.
Elsewhere in the top half of the women’s draw, last year’s runner-up Sofia Kenin moved into the last 16. The fourth-seed came from a set down against her fellow American Jessica Pagula to win 4-6, 6-1, 6-4.
Fifth seed Elina Svitolina slumped against Barbora Krejcikova. It finished 6-3, 6-2 to the 25-year-old Czech who notched up her second consecutive run to the last16.
Ons Jabeur also reached the last 16 for the second year on the trot. The 26-year-old Tunisian beat Magda Linette from Poland 3-6, 6-0, 6-1. And the 2018 finalist Sloane Stephens also advanced. She dispatched Karolina Muchova 6-3, 7-5.
